The standard Laplacian

Uwe Semmelmann
(Univeristy of Stuttgart)
AaDAG seminar
Wednesday, 11 October, 2017, at 14:30-15:30, in Aud. D1 (1531-113)
Abstract:
The standard Laplace operator is a generalization of the Hodge-Laplace operator on differential forms to arbitrary geometric vector bundles. Alternatively it can be seen as a generalization of the Casimir operator acting on sections of homogeneous vector bundles over symmetric spaces to general Riemannian manifolds.

In my talk I will discuss the definition of the standard Laplace operator and its universal properties. The main result of my talk will be a commutator formula, showing that the standard Laplace operator commutes with a large class of natural first order differential operators. This result will be illustrated in several examples. In a particular for the case of nearly Kähler manifolds.

My talk is based on a joint article with G. Weingart.

AaDAG seminar:   Aa rhus  D ifferential  A lgebraic  G eometry seminar
Organised by: QGM
Contact person: Andrew Swann