Einstein Kaehler submanifolds of a complex linear or hyperbolic space
type: Item
instance of: scholarly article
title: Einstein Kaehler submanifolds of a complex linear or hyperbolic space
zbMATH Open document ID: 0648.53031
author: Masaaki Umehara
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1987-01-01T00:00:00Z
review text: The author proves that every Einstein Kaehler submanifold of \({\mathbb{C}}^ n\) or \({\mathbb{C}}H^ n\) (the complex hyperbolic space of negative constant holomorphic sectional curvature) is always totally geodesic. He uses in his proof some previous results (by himself) on the so-called ``diastasis'' associated to a metric, a notion introduced by \textit{E. Calabi} in Ann. Math., II. Ser. 58, 1-23 (1953; Zbl 0051.131)].
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 4058350
zbMATH Keywords: Einstein Kaehler submanifold
zbMATH Keywords: totally geodesic
reviewed by: Joan Girbau
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228285
OpenAlex ID: W2040679968
cites work: Isometric imbedding of complex manifolds
cites work: Einstein hypersurfaces in a Kählerian manifold of constant holomorphic curvature
cites work: Q3040034
cites work: Differential geometry of complex hypersurfaces
cites work: Hypersurface with parallel Ricci tensor in a space of constant holomorphic sectional curvature
cites work: Einstein Kähler submanifolds with codimension 2 in a complex space form
cites work: Kaehler submanifolds of complex space forms
cites work: Diastases and real analytic functions on complex manifolds
Wikidata QID: Q125874665
DOI: 10.2748/TMJ/1178228285
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description: scientific article; zbMATH DE number 4058350