Search Results (51)

We find restrictions on a trans-Sasakian structure $\left(F,\mathbf{u},\gamma ,\alpha ,\beta \right)$ on a 3-dimensional Riemannian manifold $\left(M^3,g\right)$ so that $\left(M^3,g\right)$ is homothetic to a Sasakian manifold. In that, first we show that if the vector $\mathbf{u}$ of the trans-Sasakian structure $\left(F,\mathbf{u},\gamma ,\alpha ,\beta \right)$ on a 3-dimensional Riemannian manifold $\left(M^3,g\right)$ is an affine conformal vector with affine potential $\alpha \ne 0$ and the condition $\mathbf{u}\left(\alpha \right)=-{\beta }^2$ holds, necessarily implies $\left(M^3,g\right)$ is homothetic to a Sasakian manifold. Similarly, it is shown that if the vector $\mathbf{u}$ of the trans-Sasakian structure $\left(F,\mathbf{u},\gamma ,\alpha ,\beta \right)$ on a 3-dimensional Riemannian manifold $\left(M^3,g\right)$ is a projective vector and the sectional curvatures of the plane sections containing $\mathbf{u}$ are positive constant, then $\left(M^3,g\right)$ is homothetic to a Sasakian manifold. Finally, we find certain generic conditions on a 3-dimensional Riemannian manifold $\left(M^3,g\right)$ possessing a trans-Sasakian structure $\left(F,\mathbf{u},\gamma ,\alpha ,\beta \right)$ so that $\left(M^3,g\right)$ is homothetic to a Sasakian manifold. Full article

We first study the f-biharmonicity of totally umbilical hypersurfaces in a Riemannian manifold of dimension $n\ge 3$ and prove that any totally umbilical proper f-biharmonic hypersurface without boundaries in a nonpositively curved manifold must be noncompact. Since biharmonic submanifolds are special cases of f-biharmonic submanifolds, our results on f-biharmonic hypersurfaces in nonpositively curved conformally flat spaces provide a natural extension of the generalized Chen’s conjecture. We then investigate the f-biharmonicity of totally umbilical hyperplanes in a conformally flat space. Next, we study f-biharmonic surfaces in a conformally flat 3-space, and for those with nonzero constant mean curvature (CMC), we provide a complete classification of them in 3-space forms. Finally, we investigate the f-biharmonicity of hypersurfaces in a conformally flat space with negative sectional curvature. Our results generalize some previous conclusions on biharmonic hypersurfaces. Full article

In-pipe robots must navigate narrow, curved passages where rigid mechanisms often require bulky steering units. Soft crawlers offer better compliance but typically rely on multiple actuators or reconfigurable contacts to achieve multi-directional motion. Drawing inspiration from biological soft crawlers that exploit directional friction and coordinated anchor–slip patterns, this study focuses on locomotion principles observed in caterpillars, water boatmen, and whirligig beetles. Based on these bioinspired concepts, we present a tendon-driven soft in-pipe robot that combines continuum bending–twisting deformation with modular anisotropic friction pads (AFPs), enabling three locomotion modes using only two motors. AFP inclination, curvature, and ridge geometry were optimized through friction tests, constant-curvature modeling, and finite element analysis to enhance directional adhesion on flat and curved surfaces. A deformation-based locomotion framework was developed to couple tendon actuation with friction orientation, achieving longitudinal crawling, transverse translation, in-place rotation, and smooth transitions via programmed twisting. Driving experiments demonstrated repeatable anchor–slip locomotion with average speeds of 28.6 mm/s, 15.7 mm/s, and 11.5°/s for the three modes. Pipe tests in straight, curved, and T-junction sections further validated stable contact and reliable gait transitions. These findings highlight the potential of friction-programmed continuum robots as compact, bioinspired platforms for advanced in-pipe inspection and diagnostic tasks. Full article

Train track occupancy detection is essential for railway operation safety and dispatching, yet GNSS-based positioning and track matching can degrade or fail in turnouts and station yards due to multipath, interference, and dense track layouts. This paper presents an IMU-only method to discriminate track-switching events during turnout passage by exploiting the transient change in heading angular velocity. The Z-axis gyroscope measurement (approximately aligned with the track-plane normal) is used as a heading-rate proxy, and a lightweight indicator is constructed from the difference between a short-window moving average and the full-run mean. The full-run mean further serves as an in situ approximation of the gyroscope zero bias, alleviating the need for pre-calibration and improving robustness to systematic drift. A fixed discrimination threshold is determined from stationary gyroscope noise statistics, and the minimum effective operating speed is derived by combining gyro noise characteristics with the kinematic relationship among train speed, turnout curvature radius, and heading rate. Field experiments conducted from January to April 2025 on three railway sections covering 27 turnouts (300 turnout-passage events) show that, using a constant threshold $T_0=0.002\mathrm{rad}/\mathrm{s}$, the proposed method achieves 100% track-switching discrimination accuracy within 5–40 km/h, without requiring track maps, GNSS, or prior databases. Full article

In this paper, we examine Ricci–Bourguignon solitons on locally decomposable golden Riemannian manifolds of constant golden sectional curvature. First, we establish an explicit expression for the soliton constant in terms of the golden structure and the Bourguignon parameter. Second, we explore the geometry of these solitons when the potential vector fields are Killing, conformal Killing, homothetic, or concurrent. Finally, we initiate the study of golden Ricci–Bourguignon solitons, determine their soliton constants, and examine their properties under the specific potential vector fields. Full article

This review develops a materials-to-clinic framework for patient-specific, functionally graded (FG) NiTi shape memory alloy (SMA) rods as a complementary paradigm for scoliosis correction that targets durable alignment with motion preservation. The article synthesizes the thermomechanical basis of NiTi (thermoelastic martensitic transformation, near constant superelastic plateau, and hysteretic damping) while leveraging additive manufacturing (AM) capabilities to spatially program transformation temperatures (e.g., A_f), effective stiffness, and geometric inertia along the rod. Consolidated process–structure–property linkages are provided for the PBF-LB, DED, and BJAM routes, together with contamination and composition-control strategies (mitigation of Ni volatilization; management of O/C uptake; gradient heat treatments) and segment-level quality assurance (DSC mapping, micro-CT, EBSD/indentation, and bench bending/torsion in physiologic media). Building on clinical curve classification, the methodology formalizes a grading mask and target moment vector that drive multi-objective optimization of the segmental A_f, relative density/architecture, and cross-section, followed by route-specific build plans and acceptance tolerances. A phenomenological constitutive description provides the forward map from local design variables to temperature-dependent moment–curvature loops for finite element verification and uncertainty control. Surgical handling and activation policies are codified (cold shaping in martensite and controlled intra-/postoperative warming within tissue-safe bounds), and a translational roadmap is outlined, encompassing prospective calibration of classification-to-design mappings, AM process maps with in situ monitoring, digital twin planning, and long-horizon fatigue/corrosion protocols. The proposed graded structures provide an adaptive transformation temperature gradient and tunable mechanical response, representing an important design direction toward 3D-printed, patient-specific SMA rods for durable, adjustable, and efficient scoliosis correction. Full article

The magnonic activity refers to a chiral effect in the field of magnetization dynamics that exhibits a high degree of analogy to optical activity. It manifests as the azimuthal continuous rotation of standing-wave nodes in the cross-section of spin waves during propagation in ferromagnetic nanowire waveguides. The study employs micromagnetic simulation methods to theoretically investigate the influence of the interfacial Dzyaloshinskii–Moriya interaction (iDMI) on the magnonic activity in longitudinally magnetized ferromagnetic nanotubes. The results demonstrate that iDMI-induced chirality effectively controls the magnonic activity’s rotatory power, which relies on the values of the iDMI constant D (from $-0.5 \mathrm{m}\mathrm{J}/{\mathrm{m}}^2$ to $1 \mathrm{m}\mathrm{J}/{\mathrm{m}}^2$). Additionally, nanotube thickness variations (from 3 nm to 15 nm) alter effective curvature, further influencing the rotatory power of the magnonic activity. Numerical simulations and semi-analytical calculations show excellent agreement, providing a theoretical foundation for chiral spin-wave manipulation in 3D curved nanostructures. Full article

Structures with slender cylindrical geometries, such as subsea power cables are critical components of infrastructure systems. These structures are prone to bending deformation under load, which can ultimately cause structural failure. In this study, distributed optical fibre sensors are used to monitor the bending deformation in slender cylindrical structures. Brillouin optical time-domain reflectometry-based strain sensing was used to experimentally study three-point bending and approximately constant curvature bending of a 6 m long circular hollow section (CHS). Optical fibres were attached to the outer surface of the CHS in two different configurations: parallel to the longitudinal axis and helically wound around the CHS. Strain responses due to changing magnitudes of deformation and changing orientation of the optical fibre around the circumference of the CHS were studied. A finite element model was employed to simulate and interpret the observed strain responses. A strain response inverse analysis was conducted using the strain data obtained from the experimental study to reconstruct the deformed shapes of the CHS. Both the longitudinally aligned and helically wound fibres showed distinct strain profiles that differentiate the three-point bending and constant curvature bending behaviours. The results revealed the ability of optical fibre sensing to evaluate the type; magnitude; and orientation of the bending deformations. This fundamental understanding supports the design of sensing systems for critical cylindrical infrastructure. Full article

This paper presents a combined theoretical, numerical, and experimental analysis to investigate the lateral plastic crushing behavior and energy absorption of circular and non-circular thin-walled rings between two rigid plates. Theoretical solutions incorporating both linear material hardening and power-law material hardening models are solved via numerical shooting methods. The theoretically predicted force-denting displacement relations agree excellently with both FEA and experimental results. The FEA simulation clearly reveals the coexistence of an upper moving plastic region and a fixed bottom plastic region. A robust automatic extraction method of the fully plastic region at the bottom from FEA is proposed. A modified criterion considering the unloading effect based on the resultant moment of cross-section is proposed to allow accurate theoretical estimation of the fully plastic region length. The detailed study implies an abrupt and almost linear drop of the fully plastic region length after the maximum value by the proposed modified criterion, while the conventional fully plastic criterion leads to significant over-estimation of the length. Evolution patterns of the upper and lower plastic regions in FEA are clearly illustrated. Furthermore, the distribution of plastic energy dissipation is compared in the bottom and upper regions through FEA and theoretical results. Purely analytical solutions are formulated for linear hardening material case by elliptical integrals. A simple algebraic function solution is derived without necessity of solving differential equations for general power-law hardening material case by adopting a constant curvature assumption. Parametric analyses indicate the significant effect of ovality and hardening on plastic region evolution and crushing force. This paper should enhance the understanding of the crushing behavior of circular and non-circular rings applicable to the structural engineering and impact of the absorption domain. Full article

The current work establishes the geometrical bearing for hypersurfaces in a Golden Riemannian manifold with constant golden sectional curvature with respect to k-almost Newton-conformal Ricci solitons. Moreover, we extensively explore the immersed r-almost Newton-conformal Ricci soliton and determine the sufficient conditions for total geodesicity with adequate restrictions on some smooth functions using mathematical operators. Furthermore, we go over some natural conclusions in which the gradient k-almost Newton-conformal Ricci soliton on the hypersurface of the Golden Riemannian manifold becomes compact. Finally, we establish a Schur’s type inequality in terms of k-almost Newton-conformal Ricci solitons immersed in Golden Riemannian manifolds with constant golden sectional curvature. Full article

The main objective of this paper is to investigate the properties related to the sectional curvatures of a Kähler golden manifold, an almost Hermitian golden manifold whose almost complex golden structure is parallel with respect to the Levi–Civita connection. Under certain conditions, we prove that a Kähler golden manifold with constant sectional curvature is flat. We introduce the concepts of $\Phi$-holomorphic sectional curvature and $\Phi$-holomorphic bi-sectional curvature on a Kähler golden manifold, and compare them respectively with the holomorphic sectional curvature and holomorphic bi-sectional curvature on a Kähler manifold. Full article

This paper investigates compact Riemannian hypersurfaces immersed in $(n+1)$-dimensional Riemannian or Lorentzian manifolds that admit concircular vector fields, also known as closed conformal vector fields (CCVFs). We focus on the support function of the hypersurface, which is defined as the component of the conformal vector field along the unit-normal vector field, and derive an expression for its Laplacian. Using this, we establish integral formulae for hypersurfaces admitting CCVFs. These results are then extended to compact Riemannian hypersurfaces isometrically immersed in Riemannian or Lorentzian manifolds with constant sectional curvatures, highlighting the crucial role of CCVFs in the study of hypersurfaces. We apply these results to provide characterizations of compact Riemannian hypersurfaces in Euclidean space ${\mathbb{R}}^{n+1}$, Euclidean sphere $S^{n+1}$, and de Sitter space $S_1^{n+1}$. Full article

In this paper, we examine torse-forming vector fields to characterize extrinsic spheres (that is, totally umbilical hypersurfaces with nonzero constant mean curvatures) in Riemannian and Lorentzian manifolds. First, we analyze the properties of these vector fields on Riemannian manifolds. Next, we focus on Ricci solitons on Riemannian hypersurfaces induced by torse-forming vector fields of Riemannian or Lorentzian manifolds. Specifically, we show that such a hypersurface in the manifold with constant sectional curvature is either totally geodesic or an extrinsic sphere. Full article

In this work, we consider Pythagorean triples and quadruples using fundamental form matrices of hypersurfaces in three- and four-dimensional space forms and illustrate various figures. Moreover, we generalize that an immersed hypersphere $M^n$ with radius r in an $(n+1)$-dimensional Riemannian space form ${\mathbb{M}}^{n+1}\left(\mathbf{c}\right)$, where the constant sectional curvature is $\mathbf{c}\in \{-1,0,1\}$, satisfies the $(n+1)$-tuple Pythagorean formula ${\mathcal{P}}_{n+1}$. Remarkably, as the dimension $n\to \infty$ and the fundamental form $N\to \infty$, we reveal that the radius of the hypersphere converges to $r\to {\displaystyle \frac{1}{\sqrt{2}}}$. Finally, we propose that the determinant of the ${\mathcal{P}}_{n+1}$ formula characterizes an umbilical round hypersphere satisfying $k_1=k_2=\cdots =k_n$, i.e., $H^n=K_e$ in ${\mathbb{M}}^{n+1}\left(\mathbf{c}\right)$. Full article

This study is focused on pioneering new upper bounds on mean curvature and constant sectional curvature relative to the first positive eigenvalue of the generalized Laplacian operator in the differentiable manifolds with a semi-symmetric metric connection. Multiple approaches are being explored to determine the principal eigenvalue for the generalized-Laplacian operator in closed oriented-slant submanifolds within a Sasakian space form (ssf) with a semi-symmetric metric (ssm) connection. By utilizing our findings on the Laplacian, we extend several Reilly-type inequalities to the generalized Laplacian on slant submanifolds within a unit sphere with a semi-symmetric metric (ssm) connection. The research is concluded with a detailed examination of specific scenarios. Full article