On the Spectrum of the Geodesic Flow on Spheres

  • Ivailo M. Mladenov
  • Vasil V. Tsanov
Chapter

Abstract

We propose a uniform method for derivation of the energy spectrum of the geodesic flow of the sphere S n (and hence of the Kepler problem) for all dimensions n ≥ 1. The idea is to use Marsden-Weinstein reduction in the context of equivariant cohomology. The one-dimensional case is thus covered by the general geometric quantization scheme.

Keywords

Line Bundle Cohomology Ring Geometric Quantization Equivariant Cohomology Geodesic Flow 
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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Ivailo M. Mladenov
    • 1
  • Vasil V. Tsanov
    • 2
  1. 1.Central Laboratory of BiophysicsBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Faculty of Mathematics and InformaticsSofia UniversitySofiaBulgaria

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