Geometry of Submanifolds and Homogeneous Spaces

• Main Author: Kaimakamis, George (auth)
• Other Authors: Arvanitoyeorgos, Andreas (auth)
• Format: Electronic Book Chapter
• Language: English
• Published: MDPI - Multidisciplinary Digital Publishing Institute 2020
• Subjects: warped products; vector equilibrium problem; Laplace operator; cost functional; pointwise 1-type spherical Gauss map; inequalities; homogeneous manifold; finite-type; magnetic curves; Sasaki-Einstein; evolution dynamics; non-flat complex space forms; hyperbolic space; compact Riemannian manifolds; maximum principle; submanifold integral; Clifford torus; D'Atri space; 3-Sasakian manifold; links; isoparametric hypersurface; Einstein manifold; real hypersurfaces; Kähler 2; *-Weyl curvature tensor; homogeneous geodesic; optimal control; formality; hadamard manifolds; Sasakian Lorentzian manifold; generalized convexity; isospectral manifolds; Legendre curves; geodesic chord property; spherical Gauss map; pointwise bi-slant immersions; mean curvature; weakly efficient pareto points; geodesic symmetries; homogeneous Finsler space; orbifolds; slant curves; hypersphere; ??-space; k-D'Atri space; *-Ricci tensor; homogeneous space
• Online Access: DOAB: download the publication; DOAB: description of the publication

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.