Miscellanea

  • Sorin Dragomir
  • Liviu Ornea
Part of the Progress in Mathematics book series (PM, volume 155)

Abstract

Totally umbilical submanifolds of complex space forms have been classified by B.Y. Chen&K. Ogiue, [60], cf. Theorem 1, p. 225. Their classification relies on the earlier observation (cf. [59], Prop. 3.1, p. 260) that curvature-invariant submanifolds of a complex space form are either holomorphic or totally real. In [79] one extends these ideas to submanifolds of Sasakian space forms and obtains the following:

Theorem 17.1 Let M2m+1 be an odd-dimensional totally umbilical sub-manifold of a Sasakian space form M2m+1(c), 1 < m < n. If M2m+1 is tangent to the contact vector ξ of M2n+1(c) then M2m+1 is a Sasakian space form immersed in M2n+1(c) as a totally geodesic submanifold.

Keywords

Manifold Betti 

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Sorin Dragomir
    • 1
  • Liviu Ornea
    • 2
  1. 1.Dipartimento di MatematicaUniversità degli Studi della BasilicataPotenzaItalia
  2. 2.Facultatea de MatematicaUniversitatea din BucureştiBucureştiRomania

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