Lower Bounds for the Eigenvalues of the Dirac Operator: Part I. The Hypersurface Dirac Operator |
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| Authors: | Oussama Hijazi Xiao Zhang |
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| Affiliation: | (1) Institut Élie Cartan, Université Henri Poincaré, Nancy 1, B.P. 239, 54506 Vandoeuvre-Lès-Nancy Cedex, France;(2) Institute of Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, 100080, P.R. China |
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| Abstract: | We give optimal lower bounds for the hypersurface Diracoperator in terms of the Yamabe number, the energy-momentum tensor andthe mean curvature. In the limiting case, we prove that the hypersurfaceis an Einstein manifold with constant mean curvature. |
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| Keywords: | conformal geometry Dirac operator hypersurfaces spectrum |
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