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Geometry of Submanifolds and Homogeneous Spaces
Andreas Arvanitoyeorgos and George Kaimakamis
2019-2020
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The present Special Issue of Symmetry is devoted to two important areas of global Riemannian geometry, namely submanifold theory and the geometry of Lie groups and homogeneous spaces. Submanifold theory originated from the classical geometry of curves and surfaces. Homogeneous spaces are manifolds that admit a transitive Lie group action, historically related to F. Klein's Erlangen Program and S. Lie's idea to use continuous symmetries in studying differential equations. In this Special Issue, we provide a collection of papers that not only reflect some of the latest advancements in both areas, but also highlight relations between them and the use of common techniques. Applications to other areas of mathematics are also considered.
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Keywords
- *-Ricci tensor
- *-Weyl curvature tensor
- 3-Sasakian manifold
- ??-space
- Clifford torus
- compact Riemannian manifolds
- cost functional
- D’Atri space
- Einstein manifold
- evolution dynamics
- finite-type
- formality
- generalized convexity
- geodesic chord property
- geodesic symmetries
- hadamard manifolds
- homogeneous Finsler space
- homogeneous geodesic
- homogeneous manifold
- homogeneous space
- hyperbolic space
- hypersphere
- inequalities
- isoparametric hypersurface
- isospectral manifolds
- k-D’Atri space
- Kähler 2
- Laplace operator
- Legendre curves
- links
- magnetic curves
- maximum principle
- mean curvature
- non-flat complex space forms
- Optimal Control
- orbifolds
- pointwise 1-type spherical Gauss map
- pointwise bi-slant immersions
- real hypersurfaces
- Sasaki-Einstein
- Sasakian Lorentzian manifold
- slant curves
- spherical Gauss map
- submanifold integral
- vector equilibrium problem
- warped products
- weakly efficient pareto points
Links
DOI: 10.3390/books978-3-03928-001-8Editions