Normal holonomy and Berger-type theorems

OLMOS, CARLOS

Augsburg, Alemania

Conferencia; Oberseminar Differentialgeometrie Universität Augsburg; 2009

Institut fûr Mathematik der Universtität Augsburg

The normal holonomy of a submanifold of a space form turns out to be even simpler than Riemannian holonomy. This has interesting consequences not only in submanifold geometry, but also in Riemannian geometry. In fact, the Berger holonomy theorem depends strongly on the fact that the normal holonomy has a very special form. In this talk we would like to draw the attention on some results, similar to that of Berger, in the context of submanifolds and Riemannian geometry. Finally, we will discuss some applications to naturally reductive spaces, which in particular explain the inextendibility of isotropy irreducible spaces (in the sense of Wolf and Wang-Ziller).