Results in Mathematics

, Volume 27, Issue 3–4, pp 207–226 | Cite as

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

  • Christos Baikoussis
  • David E. Blair
  • Themis Koufogiorgos


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.

Mathematics subject classification



Integral submanifolds C-parallel submanifolds 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    C. Baikoussis, D.E. Blair, Integral surfaces of Sasakian space forms, Journal of Geom. 43 (1992), 30–40.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    D.E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics, Vol 509, Berlin-Heidelberg-New York, Springer 1976.Google Scholar
  3. [3]
    F. Dillen, L. Vrancken, C-totally real submanifolds of S7(1) with non-negative sectional curvature, Math. J. Okayama Univ. 31 (1989), 227–242.MathSciNetMATHGoogle Scholar
  4. [4]
    H. Naitoh, Parallel submanifolds of complex space forms I,II, Nagoya Math. J., 90 (1983), 85–117; 91 (1983), 119-149.MathSciNetMATHGoogle Scholar
  5. [5]
    H. Naitoh, M. Takeuchi, Totally real submanifolds and symmetric bounded domains, Osaka J. Math., 19 (1982), 717–731.MathSciNetMATHGoogle Scholar
  6. [6]
    K. Oguie, On fiberings of almost contact manifolds, Kōdai Mat. Sem. Rep. 17 (1965), 53–62.CrossRefGoogle Scholar
  7. [7]
    K. Ogiue, Notes in Differential Geometry, Universidad de Granada, (Lecture Notes by O.J. Garay), (1985).Google Scholar
  8. [8]
    B. O’Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459–469.MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    D.Van Lindt, P. Verheyen, L. Verstraelen, Minimal submanifolds in Sasakian space forms, Journal of Geom. 27 (1986), 180–187.MATHCrossRefGoogle Scholar
  10. [10]
    L. Verstraelen, L. Vrancken, Pinching theorems for C-totally real submanifolds of Sasakian space forms, Journal of Geom. 33 (1988), 172–184.MathSciNetMATHCrossRefGoogle Scholar
  11. [11]
    L. Vrancken, Locally symmetric C-totally real submanifolds of S7(1), Kyungpook Mathematical Journ. 29 (1988), 167–186.MathSciNetGoogle Scholar

Copyright information

© Birkhäuser Verlag, Basel 1995

Authors and Affiliations

  • Christos Baikoussis
    • 1
  • David E. Blair
    • 1
  • Themis Koufogiorgos
    • 2
  1. 1.Themis Koufogiorgos Department of MathematicsUniversity of Ioannina IoanninaGreece
  2. 2.Department of Mathematics Michigan StateUniversity East LansingUSA

Personalised recommendations