Some curvature conditions on a para-Sasakian manifold with canonical paracontact connection
type: Item
instance of: scholarly article
title: Some curvature conditions on a para-Sasakian manifold with canonical paracontact connection
zbMATH Open document ID: 1259.53027
DOI: 10.1155/2012/395462
author: B. E. Acet
author: Erol Kiliç
author: Selcen Yüksel Perktaş
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2013-02-21T00:00:00Z
review text: Summary: We study a canonical paracontact connection on a para-Sasakian manifold. We prove that a Ricci-flat para-Sasakian manifold with respect to the canonical paracontact connection is an \(\eta\)-Einstein manifold. We also investigate some properties of the curvature tensor, the conformal curvature tensor, the \(W_2\)-curvature tensor, the concircular curvature tensor, the projective curvature tensor, and the pseudo-projective curvature tensor with respect to the canonical paracontact connection on a para-Sasakian manifold. It is shown that a concircularly flat para-Sasakian manifold with respect to the canonical paracontact connection is of constant scalar curvature. We give some characterizations of pseudo-projectively flat para-Sasakian manifolds.
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 6137709
zbMATH Keywords: paracontact connection
zbMATH Keywords: para-Sasakian manifold
zbMATH Keywords: \(\eta\)-Einstein manifold
zbMATH Keywords: concircularly flat
zbMATH Keywords: pseudo-projectively flat
Wikidata QID: Q58705815
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/395462
OpenAlex ID: W2076462841
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DBLP publication ID: journals/ijmmsc/EftalKP12
description: scientific article; zbMATH DE number 6137709