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Annals of Global Analysis and Geometry

, Volume 3, Issue 3, pp 289–312 | Cite as

On the spectrum and the geometry of a spherical space form II

  • Friedbert Prufer
Article

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.

Keywords

Group Theory Explicit Formula Space Form Partial Answer Geometrical Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© VEB Deutscher Verlag der Wissenschaften 1985

Authors and Affiliations

  • Friedbert Prufer
    • 1
  1. 1.Department of MathematicsKarl Marx UniversityLeipzigGDR

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