Differential Geometry

• Main Author: Mihai, Ion (auth)
• Format: Electronic Book Chapter
• Language: English
• Published: MDPI - Multidisciplinary Digital Publishing Institute 2019
• Subjects: statistical structure; constant ratio submanifolds; Euclidean submanifold; framed helices; Sasakian statistical manifold; L2-harmonic forms; Hodge-Laplacian; complete connection; concircular vector field; cylindrical hypersurface; k-th generalized Tanaka-Webster connection; Casorati curvature; symplectic curves; generalized 1-type Gauss map; rectifying submanifold; manifold with singularity; ruled surface; Minkowski plane; compact complex surfaces; conjugate connection; T-submanifolds; L2-Stokes theorem; inextensible flow; shape operator; generalized normalized ?-Casorati curvature; Sasakian manifold; centrodes; circular helices; non-flat complex space form; invariant; Frenet frame; Darboux frame; trans-Sasakian 3-manifold; singular points; symplectic curvatures; Kähler-Einstein metrics; conjugate symmetric statistical structure; sectional ?-curvature; circular rectifying curves; developable surface; capacity; Ricci soliton; Reeb flow symmetry; Minkowskian pseudo-angle; conical surface; lie derivative; position vector field; pinching of the curvatures; Hessian manifolds; Minkowskian angle; Hessian sectional curvature; Minkowskian length; lightlike surface; affine sphere; concurrent vector field; slant; affine hypersurface; anti-invariant; statistical manifolds; Ricci operator; C-Bochner tensor; Ricci curvature; real hypersurface; scalar curvature; framed rectifying curves
• Online Access: DOAB: download the publication; DOAB: description of the publication

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.