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Integral submanifolds of sasakian space forms \( {\bar M}^{7}(k) \)

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Abstract

This paper gives a classification of 3-dimensional integral submanifolds of 7-dimensional Sasakian space forms for which the covariant derivative of the second fundamental form is parallel to the characteristic vector field. In the case of the 7-sphere, when the submanifold is flat, the position vector is given explicitly. In the case of negative ϕ-sectional curvature an interesting example is given in detail.

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Authors and Affiliations

  1. Themis Koufogiorgos Department of Mathematics, University of Ioannina Ioannina, 45110, Greece

    Christos Baikoussis & David E. Blair

  2. Department of Mathematics Michigan State, University East Lansing, MI 48824, USA

    Themis Koufogiorgos

Authors
  1. Christos Baikoussis
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  2. David E. Blair
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  3. Themis Koufogiorgos
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Dedicated to professor Katsumi Nomizu on the occasion of his 70th birthday

Research supported by E.E.C. contract CHRX-CT92-0050

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Baikoussis, C., Blair, D.E. & Koufogiorgos, T. Integral submanifolds of sasakian space forms \( {\bar M}^{7}(k) \) . Results. Math. 27, 207–226 (1995). https://doi.org/10.1007/BF03322826

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  • DOI: https://doi.org/10.1007/BF03322826

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