A Holonomy Theorem for 3-Forms and the Full Isometry Group of Naturally Reductive Metrics

CARLOS OLMOS

Cuernavaca

Workshop; Global Riemannian Geometry; 2008

Instituto de Matemáticas, Universidad Autónoma de México

In the first part of the talk we will survey results related to submanifolds and holonomy. We will explain a new application of these methods (joint work with Silvio Reggiani): a Simons type holonomy theorem for 3-forms. We use this result to obtain the following theorem: The full isometry group of a naturally reductive space, which is locally irreducible and not a rank one symmetric space, coincides with the affine transformations with respect to the canonical connection, which can be easily computed