Lower Bounds for the Eigenvalues of the Dirac Operator: Part II. The Submanifold Dirac Operator |
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| Authors: | Oussama Hijazi Xiao Zhang |
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| Institution: | (1) Institut Élie Cartan, Université Henri Poincaré, Nancy I, B.P. 239, 54506 Vand uvre-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: | In this paper we generalize the results of Part I to the submanifoldDirac operator. In particular, we give optimal lower bounds for thesubmanifold Dirac operator in terms of the mean curvature and othergeometric invariants as the Yamabe number or the energy-momentum tensor.In the limiting case, we prove that the submanifold is Einstein if thenormal bundle is flat. |
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| Keywords: | conformal geometry Dirac operator energy-momentum tensor spectrum submanifolds |
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