Invariant submanifolds of real hypersurfaces of complex space forms

Part of the Developments in Mathematics book series (DEVM, volume 19)


In Remark 15.1 we recalled that real hypersurfaces of a complex manifold admit a naturally induced almost contact structure F from the almost complex structure of the ambient manifold. In Theorem 21.3 we proved that if M is a complete n-dimensional CR submanifold of maximal CR dimension of a complex projective space \({\bf P}^{\frac{n+p}{2}}({\bf C})\) satisfying the condition (21.1) then M is congruent to a geodesic hypersphere \(M_{0,k}^C\) for \(k=\frac{n-1}{2}\), or to \(M(n,\theta)\), or there exists a geodesic hypersphere s of \({\bf P}^{\frac{n+p}{2}}({\bf C})\) M such that is an invariant submanifold by the almost contact structure F of S. It is easy to check that for the geodesic hypersphere \(M_{0,k}^C\) for \(k=\frac{n-1}{2}\), the following relation is satisfied


Complex Manifold Principal Curvature Contact Structure Ahler Manifold Real Hypersurface 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

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

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