Ricci solitons in \(\alpha\)-Sasakian manifolds
type: Item
instance of: scholarly article
title: Ricci solitons in \(\alpha\)-Sasakian manifolds
zbMATH Open document ID: 1247.53052
DOI: 10.5402/2012/421384
author: Gurupadavva Ingalahalli
author: C. S. Bagewadi
published in: ISRN Geometry
publication date: 2012-09-07T00:00:00Z
review text: Summary: We study Ricci solitons in \(\alpha\)-Sasakian manifolds. It is shown that a symmetric parallel second order-covariant tensor in a \(\alpha\)-Sasakian manifold is a constant multiple of the metric tensor. Using this, it is shown that if \(\mathcal L_V g + 2S\) is parallel where \(V\) is a given vector field, then \((g, V, \lambda)\) is a Ricci soliton. Further, by virtue of this result, Ricci solitons for \(n\)-dimensional \(\alpha\)-Sasakian manifolds are obtained. Next, Ricci solitons for 3-dimensional \(\alpha\)-Sasakian manifolds are discussed with an example.
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 35Q51
zbMATH DE Number: 6078638
zbMATH Keywords: second order-covariant tensor
zbMATH Keywords: parallel
zbMATH Keywords: \(\alpha\)-Sasakian manifolds
Wikidata QID: Q58690372
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.5402/2012/421384
OpenAlex ID: W1574817338
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description: scientific article; zbMATH DE number 6078638