Lower bounds for the eigenvalues of the Dirac operator |
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| Affiliation: | 1. Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany;2. Department of Mathematics, Leipzig University, 04081 Leipzig, Germany;3. School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200240, China;1. Department of Physics and Research Institute of Basic Science, Kyung Hee University, Seoul 02447, Republic of Korea;2. School of Physics, Korea Institute for Advanced Study, Seoul 02445, Republic of Korea |
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| Abstract: | On a compact Riemannian spin manifold we give new lower bounds for the eigenvalues of the Dirac operator in terms of the curvature and of the norm of an appropriate endomorphism of the tangent bundle. As a corollary, one gets all known results in this direction. The limiting-case is then studied. |
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