Berger-type theorems

OLMOS, CARLOS

Greifswald, Alemania

Conferencia; Lorentzian Geometry. Analysis and Geometry of pseudo-Riemannian Manifolds; 2009

Alfried Krupp Foundation

The normal holonomy of a submanifold of a space form, turns outto be even simpler than Riemannian holonomy(this is also true for the Lorentzian case, from a recent result of K. Lrz). This has interesting consequencesnot only in submanifold geometry,but also in Riemannian geometry. In fact, the Berger holonomytheorem depends strongly on the fact that the normal holonomy has avery special form. In this talk we would like to drawthe attention on someresults, similar to that of Berger, in the context of submanifold or Riemannian geometry (that also depend on the specialform of the normal holonomy). Finally, we will discuss some applicationsto homogeneous geometry which in particular explains the inextendibility ofisotropy irreducible spaces (in the sense of Wolf and Wang-Ziller).