Reprint

Differential Geometry

Edited by
November 2019
166 pages
  • ISBN978-3-03921-800-4 (Paperback)
  • ISBN978-3-03921-801-1 (PDF)

This book is a reprint of the Special Issue Differential Geometry that was published in

Computer Science & Mathematics
Engineering
Physical Sciences
Public Health & Healthcare
Summary

The present book contains 14 papers published in the Special Issue “Differential Geometry” of the journal Mathematics. They represent a selection of the 30 submissions.

This book covers a variety of both classical and modern topics in differential geometry. We mention properties of both rectifying and affine curves, the geometry of hypersurfaces, angles in Minkowski planes, Euclidean submanifolds, differential operators and harmonic forms on Riemannian manifolds, complex manifolds, contact manifolds (in particular, Sasakian and trans-Sasakian manifolds), curvature invariants, and statistical manifolds and their submanifolds (in particular, Hessian manifolds).

We wish to mention that among the authors, there are both well-known geometers and young researchers. The authors are from countries with a tradition in differential geometry: Belgium, China, Greece, Japan, Korea, Poland, Romania, Spain, Turkey, and United States of America. Many of these papers were already cited by other researchers in their articles. This book is useful for specialists in differential geometry, operator theory, physics, and information geometry as well as graduate students in mathematics.

Format
  • Paperback
License
© 2019 by the authors; CC BY licence
Keywords
Euclidean submanifold; position vector field; concurrent vector field; concircular vector field; rectifying submanifold; T-submanifolds; constant ratio submanifolds; Ricci soliton; Kähler–Einstein metrics; compact complex surfaces; pinching of the curvatures; statistical manifolds; Hessian manifolds; Hessian sectional curvature; scalar curvature; Ricci curvature; Minkowski plane; Minkowskian length; Minkowskian angle; Minkowskian pseudo-angle; L2-harmonic forms; Hodge–Laplacian; manifold with singularity; L2-Stokes theorem; capacity; k-th generalized Tanaka–Webster connection; non-flat complex space form; real hypersurface; lie derivative; shape operator; conical surface; developable surface; generalized 1-type Gauss map; cylindrical hypersurface; inextensible flow; lightlike surface; ruled surface; Darboux frame; C-Bochner tensor; generalized normalized δ-Casorati curvature; Sasakian manifold; slant; invariant; anti-invariant; trans-Sasakian 3-manifold; Reeb flow symmetry; Ricci operator; Sasakian statistical manifold; conjugate connection; Casorati curvature; framed rectifying curves; singular points; framed helices; centrodes; circular rectifying curves; statistical structure; affine hypersurface; affine sphere; conjugate symmetric statistical structure; sectional ∇-curvature; complete connection; symplectic curves; circular helices; symplectic curvatures; Frenet frame