Dirac operators on Lagrangian submanifolds

  • We study a natural Dirac operator on a Lagrangian submanifold of a Kähler manifold. We first show that its square coincides with the Hodge - de Rham Laplacian provided the complex structure identifies the Spin structures of the tangent and normal bundles of the submanifold. We then give extrinsic estimates for the eigenvalues of that operator and discuss some examples.

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Metadaten
Author details:Nicolas Ginoux
URN:urn:nbn:de:kobv:517-opus-5627
Publication type:Postprint
Language:English
Publication year:2004
Publishing institution:Universität Potsdam
Release date:2005/08/10
Tag:Dirac operators; Global Analysis; Lagrangian submanifolds; Spectral Geometry; Spin Geometry
Source:Journal of geometry and physics. - 52 (2004), 4, S. 480 - 498
RVK - Regensburg classification:SK 620
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
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