Lower Bounds for the Eigenvalues of the Dirac Operator: Part I. The Hypersurface Dirac Operator

Author: Hijazi O.  

Publisher: Springer Publishing Company

ISSN: 0232-704X

Source: Annals of Global Analysis and Geometry, Vol.19, Iss.4, 2001-06, pp. : 355-376

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Abstract

We give optimal lower bounds for the hypersurface Dirac operator in terms of the Yamabe number, the energy-momentum tensor and the mean curvature. In the limiting case, we prove that the hypersurface is an Einstein manifold with constant mean curvature.