Einstein Kähler submanifolds with codimension 2 in a complex space form
type: Item
instance of: scholarly article
title: Einstein Kähler submanifolds with codimension 2 in a complex space form
zbMATH Open document ID: 0592.53046
DOI: 10.1007/BF01457231
author: K. Tsukada
published in: Mathematische Annalen
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164114
review text: Einstein-Kähler hypersurfaces in complex space forms are completely classified by \textit{B. Smyth} [Ann. Math., II. Ser. 85, 246-266 (1967; Zbl 0168.196)] and \textit{S. S. Chern} [J. Differ. Geom. 1, 21-31 (1967; Zbl 0168.195)]. The author proves that the same classification holds for Einstein-Kähler submanifolds of codimension 2 in complex space forms, that is, he proves the following: Let M be an n-dimensional Einstein- Kähler submanifold immersed in \(P_{n+2}(C)\), \(C^{n+2}\) or \(D^{n+2}\). Then M is either totally geodesic or locally a complex hyperquadric in some \(P_{n+1}(C)\) in \(P_{n+2}(C)\).
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 3951494
zbMATH Keywords: Einstein-Kähler submanifolds
zbMATH Keywords: complex space forms
zbMATH Keywords: totally geodesic
zbMATH Keywords: complex hyperquadric
MaRDI profile type: Publication
cites work: Einstein hypersurfaces in a Kählerian manifold of constant holomorphic curvature
cites work: On a 2-Dimensional Einstein Kaehler Submanifold of a Complex Space Form
cites work: On locally symmetric Kaehler submanifolds in a complex projective space
cites work: Differential geometry of Kaehler submanifolds
cites work: Differential geometry of complex hypersurfaces
description: scientific article; zbMATH DE number 3951494