Submanifolds and holonomy

CARLOS ENRIQUE OLMOS

Brno

Conferencia; Differential Geometry and its Applications; 2016

Masaryk University/supported by Elsevier Editorial

http://eduart.math.muni.cz/recordings/web/ukAT-SXts-GP6B/ Abstract (Invited Plenary Speaker): in this lecture we will give a survey on Submanifolds and Holonomy.We will put into perspective the central results of the theory.There is a subtle relation between the normal holonomy of Euclidean submani-folds and the Riemannian holonomy. In particular, by means of submanifold geo-metry, with normal holonomy ingredients, one can give applications to Riemanniangeometry: a geometric proof of the Berger holonomy theorem and a proof of theso-called skew-torsion holonomy theorem (with interesting consequences for nat-urally reductive spaces). On the other hand, the Simons theorem on holonomysystems has a recent interesting application (C.O.-J.Berndt) to the classical prob-lem of studying maximal dimensional totally geodesic submanifolds of symmetricspaces and the determination of the so-called Onishchick index.We will also present some new results in the theory, including some progress tothe so-called normal holonomy conjecture for orbits (C.O.-R.Ria~no).