Submanifolds and Holonomy

OLMOS, CARLOS

Cruz Chica, La Cumbre, Córdoba, Argentina

Workshop; Sixth Workshop on Lie Theory and Geometry; 2007

FaMAF-Conicet

The holonomy group, i.e. the group obtained by parallel displacement along based loops, of thenormal connection turn out to be a very important tool for studing submanifold geometry inEuclidean or Hilbert space. Normal holonomy is close related to Riemannian holonomy, since itcan be used for giving a geometric proof of the Berger holonomy theorem. In this talk we will ¯rstsurvey some results related to normal holonomy and to the study of orbits from a geometric pointof view. In the last part of the talk we will refer to some new general results which are related tonormal holonomy.