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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.
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Keywords
- affine hypersurface
- affine sphere
- anti-invariant
- C-Bochner tensor
- capacity
- Casorati curvature
- centrodes
- circular helices
- circular rectifying curves
- compact complex surfaces
- complete connection
- concircular vector field
- concurrent vector field
- conical surface
- conjugate connection
- conjugate symmetric statistical structure
- constant ratio submanifolds
- cylindrical hypersurface
- Darboux frame
- developable surface
- Euclidean submanifold
- framed helices
- framed rectifying curves
- Frenet frame
- generalized 1-type Gauss map
- generalized normalized ?-Casorati curvature
- Hessian manifolds
- Hessian sectional curvature
- Hodge–Laplacian
- inextensible flow
- invariant
- k-th generalized Tanaka–Webster connection
- Kähler–Einstein metrics
- L2-harmonic forms
- L2-Stokes theorem
- lie derivative
- lightlike surface
- manifold with singularity
- Minkowski plane
- Minkowskian angle
- Minkowskian length
- Minkowskian pseudo-angle
- non-flat complex space form
- pinching of the curvatures
- position vector field
- real hypersurface
- rectifying submanifold
- Reeb flow symmetry
- Ricci curvature
- Ricci operator
- Ricci soliton
- ruled surface
- Sasakian manifold
- Sasakian statistical manifold
- scalar curvature
- sectional ?-curvature
- shape operator
- singular points
- slant
- statistical manifolds
- statistical structure
- symplectic curvatures
- symplectic curves
- T-submanifolds
- trans-Sasakian 3-manifold
Links
DOI: 10.3390/books978-3-03921-801-1Editions
