Jacobi fields on normal homogeneous Riemannian manifolds

Abstract

We prove that a normal homogeneous space with the property that every Jacobi field along a geodesic vanishing at two points is the restriction of a Killing field along that geodesic is a globally symmetric space.

This paper has been withdrawn by the author, due to a crucial error in the proof of Lemma 1, which completely invalidates the proof of Theorem 1