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Annals of Global Analysis and Geometry

, Volume 3, Issue 3, pp 313–327 | Cite as

Cut locus of the B-spheres

  • Célestin Rakotoniaina
Article

This paper studies the geometry of a family of homogeneous riemannian metrics on odd-dimensional spheres. For some metrics of the family the cut locus coincides with the first conjugate locus. For the others these two sets do not coincide but intersect.

Keywords

Group Theory Riemannian Metrics Conjugate Locus Homogeneous Riemannian Metrics 
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References

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    Kobayashi, N. and Nomizu, K. Foundations of differential geometry I and II. New York, Interscience.Google Scholar
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    Sakai, T. Cut loci of Berger's spheres. Hokkaido Math. Jour. 10(1981) 143–155.Google Scholar
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    Ziller, W. The Jacobi equation on naturally reductive compact Riemannian homogeneous spaces. Comment. Math. Helvetici. 52 (1977) 573–590.Google Scholar

Copyright information

© VEB Deutscher Verlag der Wissenschaften 1985

Authors and Affiliations

  • Célestin Rakotoniaina
    • 1
  1. 1.U.E.R. de mathématiquesUniversité Paris VII 2Paris Cedex 05(France)

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