Homogeneity and curvatures of geodesic spheres
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.
scientific article; zbMATH DE number 5118927
scientific article