Holonomy of homogeneous vector bundles and polar representations

CARLOS OLMOS; MARCOS SALVAI

INDIANA UNIVERSITY MATHEMATICS JOURNAL

INDIANA UNIV MATH JOURNAL

Lugar: Indiana; Año: 1995 vol. 44 p. 1007 - 1015

0022-2518

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