Natural Intrinsic Geometrical Symmetries

Abstract

A proposal is made for what could well be the most natural symmetrical Riemannian spaces which are homogeneous but not isotropic, i.e. of what could well be the most natural class of symmetrical spaces beyond the spaces of constant Riemannian curvature, that is, beyond the spaces which are homogeneous and isotropic, or, still, the spaces which satisfy the axiom of free mobility.

Theorem 20 is corrected and References [13, 14] are added

References in corpus (5)

• Isoparametric and Dupin Hypersurfaces
• All superconformal surfaces in \R^4 in terms of minimal surfaces
• A proof of the DDVV conjecture and its equality case
• Remarks on an inequality involving the normal scalar curvature
• Submanifolds of codimension two attaining equality in an extrinsic inequality

Cited by in corpus (5)

• On warped product manifolds satisfying some pseudosymmetric type conditions
• Curvature properties of Vaidya metric
• Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups
• Curvature properties of interior black hole metric
• On generalized Robertson-Walker spacetimes satisfying some curvature condition