Submanifolds in Metric Manifolds

© 2024 by the authors; CC BY-NC-ND license

Riemannian submersion; submanifold; almost-contact metric manifold; Ricci soliton; warped product submanifolds; complex projective spaces; homology groups; homotopy; sphere theorems; stable currents; kinetic energy; warped product submanifolds; complex space form; Homology groups; sphere theorem; stable currents; Dirichlet energy; schouten tensor; Z-symmetric tensor; codazzi type tensor; Z symmetric spacetimes; Reeb-flow-invariant ∗-Ricci operator; Reeb-parallel ∗-Ricci operator; semi-symmetric ∗-Ricci tensor; singular-unit normal vector field; first natural connection; affine connection; natural connection; Riemannian Π-manifolds; information geometry; nearly Kähler statistical manifold; nearly Sasakian statistical manifold; almost product structure; almost complex structure; Φ_α,p structure; Riemannian manifold; submanifold; Gibbs–Helmholtz equation; free energy; pressure; volume; temperature; Boltzmann–Gibbs–Shannon entropy; heat (thermal) capacity; thermal pressure coefficient; chemical thermodynamics; (pseudo-)Riemannian manifold; Codazzi pair; statistical manifold; quasi-statistical manifold; Schouten–van Kampen connection; tangent bundle; general natural metric; Chi ratio; golden structure; meta-Golden structure; lightlike hypersurface; n/a