L’Enseignement Mathématique, Revue Internationale, 2-4, rue du Lièvre, CH-1227 Carouge (Suisse)
Abstract
We survey applications of holonomic methods to the
study of submanifold geometry, showing the consequences of
some sort of extrinsic version of de Rham decomposition and Berger's Theorem, the so-called Normal Holonomy Theorem.
At the same time, from geometric methods in submanifold theory we sketch very strong applications to the holonomy of Lorentzian manifolds. Moreover we give a conceptual
modern proof of a result of Kostant for homogeneous spaces
