Submanifolds and holonomy

OLMOS, CARLOS

Londres

Seminario; Geometry Seminar King's College London/University College London; 2013

King's College London/University College London

Submanifolds and Holonomy --- Carlos Olmos of Universidad Nacional de Cordoba When Tue, January 22, 2013, 11am – 12pm Where Room 707, Department of Mathematics, UCL, 25 Gordon Street, WC1H 0AY (map) Description The holonomy of the normal connection turns out to be very useful in Euclidean submanifold geometry. There is also a subtle link between normal holonomy and Riemannian holonomy, in the sense that using Euclidean submanifold geometry, with normal holonomy ingredients, one can give a geometric proof of the Berger/Simons Holonomy Theorem. Moreover, one can extend this result to the so-called Skew-Symmetric Holonomy Theorem with application to naturally reductive homogeneous spaces. We will survey on old and new results in the theory. In the last part of the talk, we will define, inspired in our previous results, the so-called index of symmetry of a Riemannian manifold and we will show some results for naturally reductive spaces (joint work with Reggiani and Tamaru).