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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
17/1997

Symplectic Dirac Operators on Kähler Manifolds

Katharina Habermann

Abstract

The notion of symplectic spinors over a symplectic manifold was already introduced by B. Kostant in 1974 as a tool in his theory of geometric quantization. We observed that it is possible to define canonical symplectic Dirac operators acting on symplectic spinor fields in a similar way as one knows it from the Dirac operator on Riemannian manifolds.

In this paper we study symplectic Dirac operators provided that the underlying manifold is a Kähler manifold with the Kähler form as symplectic structure.

Received:
Jul 23, 1997
Published:
Jul 23, 1997