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Proceedings of the American Mathematical Society

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

 

 

The spectrum of the Laplacian for $ 1$-forms


Author: Shûkichi Tanno
Journal: Proc. Amer. Math. Soc. 45 (1974), 125-129
MSC: Primary 58G15; Secondary 53C20
DOI: https://doi.org/10.1090/S0002-9939-1974-0343321-8
MathSciNet review: 0343321
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Abstract: Let $ (M,g)$ and $ (M',g')$ be compact orientable Riemannian manifolds with the same spectrum of the Laplacian for $ 1$-forms. We prove that, for $ \dim M = 2,3,16,17, \cdots ,93,(M,g)$ is of constant curvature if and only if $ (M',g')$ is so.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0343321-8
Keywords: Spectrum, Laplacian, constant curvature, Weyl conformal curvature tensor, Bochner curvature tensor
Article copyright: © Copyright 1974 American Mathematical Society