Submanifolds, holonomy and homogeneous geometry

CARLOS ENRIQUE OLMOS

San Pablo

Conferencia; Modern Trends in Differential Geometry (ICM 2018 Satellite Conference); 2018

Institute of Mathematics and Statistics University of São Paulo

This will be, mainly, an expository talk. We will intend to give a panorama about the main results andtechniques in Euclidean submanifold geometry, which are related to the normal holonomy. These results,surprinsingly, have applications in Riemannian and homogeneous geometry. In the last part we will commenton some new results, in homogeneous geometry, related to the nullity of the curvature tensor (with Di Scalaand Vittone) and to the so-called Onishchik index of a symmetric space (with Berndt, and Rodr´ıguez Carreo).We will also refer to some interesting open problems in the area.