Holonomy of homogeneous vector bundles and polar representations

OLMOS, CARLOS; SALVAI, MARCOS

INDIANA UNIVERSITY MATHEMATICS JOURNAL

INDIANA UNIV MATH JOURNAL

Año: 1995 vol. 44 p. 1007 - 1015

0022-2518

Given a homogeneous vector bundle with a connection, we are concerned with the computation of its holonomy group using the homogeneous structure. In the case of the normal bundle of an irreducible homogeneous submanifold of euclidean space, we obtain that the Lie algebra of the normal holonomy group is algebraically generated by the projection to the normal space at a point of the corresponding Killing fields of the ambient space.