CR Submanifolds of Complex Projective Space pp 151-161 | Cite as

# Invariant submanifolds of real hypersurfaces of complex space forms

## Abstract

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

## Keywords

Complex Manifold Principal Curvature Contact Structure Ahler Manifold Real Hypersurface## Preview

Unable to display preview. Download preview PDF.