On real hypersurfaces of a complex projective space
Copyright policy )On real hypersurfaces of a complex projective space
In this article the authors continue their work on real hypersurfaces in complex projective spaces [part I, see Math. Z. 202, 299-311 (1989; Zbl 0661.53015), part II, see Tsukuba J. Math. 15, 547-561 (1991; Zbl 0762.53039)]. The main purpose of this paper is to provide sufficient and necessary conditions for a real hypersurface \(M\) of a complex projective space \(P_ n(\mathbb{C})\) to be locally a geodesic hypersphere of \(P_ n(\mathbb{C})\). These conditions consist of certain relations which must be satisfied by the covariant derivative of the Ricci tensor of \(M\) or by the curvature operator of \(M\) acting on the Ricci tensor or the shape operator of \(M\) as a derivation.
- Saitama University Japan
- DigiZeitschriften Germany
- Kumamoto University Japan
Local submanifolds, Local differential geometry of Hermitian and Kählerian structures, second fundamental form, non-homogeneous real hypersurfaces, Global submanifolds, homogeneous real hypersurfaces, complex projective spaces, Article, complex projective space, 510.mathematics, real hypersurfaces, parallel second fundamental form, geodesic hypersphere
Local submanifolds, Local differential geometry of Hermitian and Kählerian structures, second fundamental form, non-homogeneous real hypersurfaces, Global submanifolds, homogeneous real hypersurfaces, complex projective spaces, Article, complex projective space, 510.mathematics, real hypersurfaces, parallel second fundamental form, geodesic hypersphere
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