On \({\varphi}\)-Einstein contact Riemannian manifolds
type: Item
instance of: scholarly article
title: On \({\varphi}\)-Einstein contact Riemannian manifolds
zbMATH Open document ID: 1193.53112
author: Jong Taek Cho
author: Jun-ichi Inoguchi
published in: Mediterranean Journal of Mathematics
publication date: 2010-06-29T00:00:00Z
review text: Let \(M\) be a Riemannian manifold which is equipped with an almost contact metric structure \((\varphi,\xi,\eta,g)\). Define the \(\varphi\)-Ricci tensor \(\rho^\varphi\) of \(M\) by \(2\rho^\varphi(X,Y) =\) symmetric part of trace \(R(X,\varphi Y)\varphi\) and a tensor \(g^\varphi\) by \(g^\varphi(X,Y) = g(\varphi X, \varphi Y)\). The manifold \(M\) is said to be \(\varphi\)-Einstein if \(\rho^\varphi = \lambda g^\varphi\) for some \(\lambda \in {\mathbb R}\). The authors prove some general properties of \(\varphi\)-Einstein manifolds and study in more detail such manifolds in dimension \(3\). Every real hypersurface in a complex space form inherits an almost contact metric structure from the metric and complex structure of the ambient space. The authors investigate the \(\varphi\)-Einstein condition on such real hypersurfaces, and derive partial classifications. In the final part of this paper the authors investigate the \(\varphi\)-Einstein condition on unit tangent sphere bundles.
reviewed by: Jürgen Berndt
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53D10
zbMATH DE Number: 5728333
zbMATH Keywords: almost contact metric manifold
zbMATH Keywords: Einstein manifold
zbMATH Keywords: real hypersurface
zbMATH Keywords: complex space form
zbMATH Keywords: unit tangent sphere bundle
MaRDI profile type: Publication
full work available at URL: s00009-010-0049-9
OpenAlex ID: W1976436294
Wikidata QID: Q115390432
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DOI: 10.1007/S00009-010-0049-9
description: scientific article; zbMATH DE number 5728333