On the Spectral Rigidity of CP n

Domenico Perrone
1988 Proceedings of the American Mathematical Society  
Complex projective space CPn 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 / 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
more » ... a characterization of CP2 by the spectrum of the Laplacian on 1-forms is given. . Primary 53C55; Secondary 58G25. Key words and phrases. Spectrum of the Laplacian, Kaehler manifolds, complex projective space. This work was financed by funds of M.P.I.
doi:10.2307/2046809 fatcat:yf2s4qrhera57mvk5drvati2yy