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Hypersurfaces of a sphere with parallel shape operator

  • Mirjana Djorić
  • Masafumi Okumura
Chapter
Part of the Developments in Mathematics book series (DEVM, volume 19)

Abstract

In [53] P. J. Ryan considered hypersurfaces of real space forms and specifically, he gave a complete classification of hypersurfaces in the sphere which satisfy a certain condition. The condition that the shape operator is parallel is its special case. In this section we give the proof of this classification (in the specific case \(\nabla_XA=0\)) and furthermore, we show that the algebraic condition (13.5) on the shape operator implies that it is parallel.

Keywords

Riemannian Manifold Orthonormal Basis Constant Curvature Shape Operator Complex Projective Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.University of BelgradeBelgradeSerbia
  2. 2.Saitama UniversitySaitamaJapan

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