On the spectrum and the geometry of a spherical space form II |
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Authors: | Friedbert Prufer |
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Affiliation: | (1) Department of Mathematics, Karl Marx University, 7010 Leipzig, GDR |
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Abstract: | In this paper certain relations between the numerical coefficients of the Poisson formula of Part I and geometrical data of a spherical space form M, dim M = 2m+1 are investigated. The results yield an explicit relation between the spectrum of M and the Poincaré map of certain closed geodesics of M. Furthermore, explicit formulas for the multiplicities of the eigenvalues of the Laplacian of M are derived by means of the Poisson formula. At the end of the paper the information about M is examined which is contained in a finite part of spec(M). A partial answer is given in the Corollaries 3 and 6. |
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