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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Extrinsic upper bounds for eigenvalues of Dirac-type operators


Author: N. Anghel
Journal: Proc. Amer. Math. Soc. 117 (1993), 501-509
MSC: Primary 58G25; Secondary 53C42
DOI: https://doi.org/10.1090/S0002-9939-1993-1111213-4
MathSciNet review: 1111213
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Abstract: Extrinsic estimates from above for eigenvalues of generalized Dirac operators on compact manifolds are given. They depend on the second fundamental form of any isometric immersion of the manifold in some Euclidean space and the curvature term in the Bochner-Weitzenböck formula for the square of the Dirac operator. Most of the known extrinsic upper bounds for the first eigenvalue of the Laplacian are in this way easily recovered and extended.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1111213-4
Keywords: Isometric immersion, generalized Dirac operator, eigenvalue, upper bound
Article copyright: © Copyright 1993 American Mathematical Society