Submanifolds and Holonomy

CARLOS OLMOS

Parma

Conferencia; Seminario, Dipartamento di Matematica, Università di Parma; 2017

Dipartamento di Scienze Matematiche, Universtitá di Parma

This will be mainly survey lecture 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 a geometric proof of the Berger holonomy theorem and a proof of the so-called skew-torsion holonomy theorem (with interesting applications for nat- urally reductive spaces). We will also present some new result in the theory (joint work with R. Riaño).