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On the spectral rigidity of $ {\bf C}{\rm P}\sp n$


Author: Domenico Perrone
Journal: Proc. Amer. Math. Soc. 104 (1988), 871-875
MSC: Primary 58G25; Secondary 53C55
DOI: https://doi.org/10.1090/S0002-9939-1988-0964867-5
MathSciNet review: 964867
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Abstract: Complex projective space $ C{P^n}$ with the Fubini-Study metric has recently been characterized by the spectrum of the Laplacian on $ 2$-forms. This important result was proved separately for $ n \ne 2,8$ by B. Y. Chen and L. Vanhecke, and for $ n = 2$ and $ n = 8$ by S. I. Goldberg. In this paper, we give a new proof which does not distinguish the three cases. It makes strong use of a result of S. Kobayashi and T. Ochiai, and may be applied to the spectrum of the Laplacian on $ 1$-forms. Moreover, a characterization of $ C{P^2}$ by the spectrum of the Laplacian on $ 1$-forms is given.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0964867-5
Keywords: Spectrum of the Laplacian, Kaehler manifolds, complex projective space
Article copyright: © Copyright 1988 American Mathematical Society

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