Supersymmetry and the generalized Lichnerowicz formula
Abstract
A classical result in differential geometry due to Lichnerowicz [8] is concerned with the decomposition of the square of Dirac operators defined by Clifford connections on a Clifford module ${\cal E}$\ over a Riemannian manifold $M$. Recently, this formula has been generalized to arbitrary Dirac operators [2]. In this paper we prove a supersymmetric version of the generalized Lichnerowicz formula, motivated by the fact that there is a onetoone correspondence between Clifford superconnections and Dirac operators. We extend this result to obtain a simple formula for the supercurvature of a generalized Bismut superconnection. This might be seen as a first step to prove the local index theorem also for families of arbitrary Dirac operators.
 Publication:

eprint arXiv:dgga/960100
 Pub Date:
 January 1996
 arXiv:
 arXiv:dgga/9601004
 Bibcode:
 1996dg.ga.....1004A
 Keywords:

 Mathematics  Differential Geometry
 EPrint:
 20 pages, plain tex