On \(\phi\)-recurrent generalized Sasakian-space-forms
type: Item
instance of: scholarly article
title: On \(\phi\)-recurrent generalized Sasakian-space-forms
zbMATH Open document ID: 1278.53044
DOI: 10.1134/S1995080212030146
author: Matilal Sen
author: Avijit Sarkar
published in: Lobachevskii Journal of Mathematics
publication date: 2013-01-23T00:00:00Z
review text: The authors study \(\phi\)-recurrent generalized Sasakian-space-forms, i.e. almost contact metric manifolds satisfying additional conditions for the curvature tensor. In particular, the curvature tensor of such manifolds is of the form \[ \begin{multlined} R(X,Y)Z = f_1(g(Y,Z)X-g(X,Z)Y)+f_2(g(X,\phi Z)\phi Y-g(Y,\phi Z)\phi X+2 g(X,\phi Y)\phi Z)\\ +f_3(\eta(X)\eta(Z)Y-\eta(Y)\eta(Z)X+g(X,Z)\eta(Y)\xi-g(Y,Z)\eta(X)\xi)\end{multlined} \] for some functions \(f_1,f_2,f_3\). They obtain some results assuming that the dimension of the manifold is greater than \(3\) and that \(f_1-f_3\) is a non-zero constant.
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 6128345
zbMATH Keywords: \(\phi\)-recurrent
zbMATH Keywords: generalized Sasakian-space-forms
zbMATH Keywords: Einstein manifold
reviewed by: Kamil Niedzialomski
MaRDI profile type: Publication
cites work: Generalized Sasakian-space-forms
cites work: Structures on generalized Sasakian-space-forms
cites work: Contact manifolds in Riemannian geometry
cites work: SASAKIAN MANIFOLDS WITH QUASI-CONFORMAL CURVATURE TENSOR
cites work: Sasakian \(\varphi\)-symmetric spaces
cites work: Isometric immersions of Sasakian manifolds in spheres
description: scientific article; zbMATH DE number 6128345