Normal curvature of CR submanifolds of maximal CR dimension of the complex projective space |
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Authors: | M Djori? M Okumura |
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Institution: | 1.Faculty of Mathematics,University of Belgrade,Belgrade,Serbia;2.Kawasaki,Japan |
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Abstract: | We prove that there do not exist CR submanifolds Mn of maximal CR dimension of a complex projective space \({\mathbf{P}^{\frac{n+p}{2}}(\mathbf{C})}\) with flat normal connection D of M, when the distinguished normal vector field is parallel with respect to D. If D is lift-flat, then there exists a totally geodesic complex projective subspace \({\mathbf{P}^{\frac{n+1}{2}}(\mathbf{C})}\) of \({\mathbf{P}^{\frac{n+p}{2}}(\mathbf{C})}\) such that M is a real hypersurface of \({\mathbf{P}^{\frac{n+1}{2}}(\mathbf{C})}\). |
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