Semi-Kählerian submanifolds of an indefinite complex space form
type: Item
instance of: scholarly article
title: Semi-Kählerian submanifolds of an indefinite complex space form
zbMATH Open document ID: 0669.53015
author: Reiko Aiyama
author: Hisao Nakagawa
author: Young Jin Suh
published in: Kodai Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: Let \(M'\) be an indefinite Kaehlerian manifold of constant holomorphic curvature and M a semi-Kaehlerian submanifold of \(M'\). The purpose of the paper is to study the geometry of M under additional hypotheses. In {\S} 3 M is supposed to be space-like and its scalar curvature to be constant. {\S} 4 describes conditions for complete submanifolds M to be Einstein manifolds. In {\S} 5 M is an indefinite Kaehler space form, too. And the last two sections are devoted to complex Einstein hypersurfaces of \(M'\). The results mainly are obtained by thorough local investigations.
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53B35
Mathematics Subject Classification ID: 53B30
zbMATH DE Number: 4096288
zbMATH Keywords: indefinite Kaehlerian manifold
zbMATH Keywords: semi-Kaehlerian submanifold
zbMATH Keywords: complex Einstein hypersurfaces
reviewed by: Helmut Reckziegel
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138038931
OpenAlex ID: W2074650580
cites work: Complex hypersurfaces in an indefinite complex space form
cites work: Q3821235
cites work: Indefinite Kähler manifolds
cites work: Isometric imbedding of complex manifolds
cites work: Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces
cites work: Product complex sumanifold of indefinite complex space forms
cites work: Q5731354
cites work: Complex submanifolds with constant scalar curvature in a Kähler manifold
cites work: Complex Einstein hypersurfaces of indefinite complex space forms
cites work: Complex Space Forms Immersed in Complex Space Forms
cites work: On locally symmetric Kaehler submanifolds in a complex projective space
cites work: On maximal spacelike hypersurfaces in a Lorentzian manifold
cites work: Isometric immersions of Riemannian manifolds
cites work: A survey of generalized goal programming (1970-1982)
cites work: On a certain class of complex Einstein hypersurfaces in indefinite complex space forms
cites work: Some Examples of Indefinite Complete Complex Einstein Hypersurfaces Not Locally Symmetric
cites work: An extension of Calabi's rigidity theorem to complex submanifolds of indefinite complex space forms
cites work: Hypersurfaces with parallel Ricci tensor
cites work: Complex hypersurfaces with RS=0 in C\(^{n+1}\)
cites work: Flat Möbius strips of given isotopy type in \(\mathbb R^{3}\) whose centerlines are geodesics or lines of curvature
cites work: Q5546515
cites work: Harmonic functions on complete riemannian manifolds
DOI: 10.2996/KMJ/1138038931
description: scientific article; zbMATH DE number 4096288