On Infinitesimal Holonomy and Isotropy Groups
On Infinitesimal Holonomy and Isotropy Groups
We have proved in [2] that if the restricted homogeneous holonomy group of a complete Riemannian manifold is contained in the linear isotropy group at every point, then the Riemannian manifold is locally symmetric, that is, the covariant derivatives of the curvature tensor field are zero. The proof of this …