Homogeneity and curvatures of geodesic spheres
type: Item
instance of: scholarly article
title: Homogeneity and curvatures of geodesic spheres
zbMATH Open document ID: 1123.53017
author: Eduardo García-Río
author: José Carlos Díaz-Ramos
author: Lieven Vanhecke
published in: Monatshefte für Mathematik
publication date: 2007-01-26T00:00:00Z
review text: The purpose of this paper is to link the study of geodesic spheres with the investigation of scalar curvature invariants. The whole space of scalar curvature invariants is generated by the so-called Weyl invariants. For an arbitrary simple Weyl invariant on a geodesic sphere, the authors give an explicit expression of the first terms in its power series expansion as a function of the radius. By integrating that invariant, they obtain the corresponding total scalar curvature of a geodesic sphere and discuss its power series expansion. The geometrical meaning of the first terms in those expansions is studied, leading to characterizations of the two-point homogeneous spaces among Riemannian manifolds with adapted holonomy.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 5118927
zbMATH Keywords: curvature invariants
zbMATH Keywords: Damek-Ricci spaces
zbMATH Keywords: geodesic spheres
zbMATH Keywords: homogeneous spaces
zbMATH Keywords: two-point homogeneous spaces
reviewed by: Rosa Anna Marinosci
MaRDI profile type: Publication
full work available at URL: s00605-006-0385-9
OpenAlex ID: W2081319873
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DOI: 10.1007/S00605-006-0385-9
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description: scientific article; zbMATH DE number 5118927