Parallel tensors and Ricci solitons in \(N(k)\)-quasi Einstein manifolds
type: Item
instance of: scholarly article
title: Parallel tensors and Ricci solitons in \(N(k)\)-quasi Einstein manifolds
zbMATH Open document ID: 1264.53045
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2012-11-15T00:00:00Z
review text: The present paper deals with the well-known Einstein problem of finding parallel and symmetric tensors in the framework of \(N(k)\)-quasi Einstein manifolds. The main result is related to the recent theory of Ricci solitons. The author proves that if the generator of the manifold provides a Ricci soliton then it is: i) shrinking on a class of conformally flat perfect fluid space-time and on quasi-umbilical hypersurfaces, in particular unit spheres; ii) expanding if the generator is of torse-forming type.
reviewed by: Raina Ivanova
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 6107842
zbMATH Keywords: Parallel second order covariant tensor field
zbMATH Keywords: \(N(k)\)-quasi Einstein manifold
zbMATH Keywords: torse-forming vector field
zbMATH Keywords: Ricci soliton
zbMATH Keywords: perfect fluid
author: Mircea Crasmareanu
MaRDI profile type: Publication
full work available at URL: s13226-012-0022-3
OpenAlex ID: W2016115309
cites work: Recent Progress on Ricci Solitons
cites work: From the Eisenhart problem to Ricci solitons in \(f\)-Kenmotsu manifolds
cites work: Q5673532
cites work: Q3413423
cites work: Q3482483
cites work: Q4516925
cites work: \(N(k)\)-quasi Einstein manifolds satisfying certain conditions
cites work: Q3531279
cites work: Q3374788
cites work: On quasi-Einstein spacetimes
cites work: Second order parallel tensor in real and complex space forms
cites work: Q4033789
cites work: Q4006635
cites work: On the curvature of contact metric manifolds
cites work: Q5412672
cites work: Investigation of some conditions on \(N(k)\)-quasi Einstein manifolds
cites work: ON N(k)-QUASI EINSTEIN MANIFOLDS
cites work: Existence of Linear Connections with Respect to Which Given Tensor Fields are Parallel or Recurrent
cites work: Holonomy groups of indefinite metrics
DOI: 10.1007/S13226-012-0022-3
description: scientific article; zbMATH DE number 6107842