Invariant submanifolds of Sasakian manifolds admitting semisymmetric nonmetric connection
type: Item
instance of: scholarly article
title: Invariant submanifolds of Sasakian manifolds admitting semisymmetric nonmetric connection
zbMATH Open document ID: 1251.53032
DOI: 10.1155/2012/947640
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2012-10-16T00:00:00Z
review text: Summary: The object of this paper is to study invariant submanifolds \(M\) of Sasakian manifolds \(\widetilde{M}\) admitting a semisymmetric nonmetric connection, and it is shown that \(M\) admits a semisymmetric nonmetric connection. Further it is proved that the second fundamental forms \(\sigma\) and \(\overline{\sigma}\) with respect to the Levi-Civita connection and the semi-symmetric nonmetric connection coincide. It is shown that if the second fundamental form \(\sigma\) is recurrent, 2-recurrent, generalized 2-recurrent, semiparallel, pseudoparallel, and Ricci-generalized pseudoparallel and \(M\) has parallel third fundamental form with respect to the semisymmetric nonmetric connection, then \(M\) is totally geodesic with respect to Levi-Civita connection.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 6093879
zbMATH Keywords: semisymmetric nonmetric connection
zbMATH Keywords: 2-recurrent
zbMATH Keywords: generalized 2-recurrent
zbMATH Keywords: semiparallel
zbMATH Keywords: pseudoparallel
zbMATH Keywords: Ricci-generalized pseudoparallel
Wikidata QID: Q58705253
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/947640
OpenAlex ID: W2089867093
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cites work: A semi-symmetric non-metric connection on a Riemannian manifold
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DBLP publication ID: journals/ijmmsc/AnithaB12
author: B. S. Anitha
author: C. S. Bagewadi
description: scientific article; zbMATH DE number 6093879