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Commun. Korean Math. Soc. 2019; 34(1): 303-319
Online first article June 18, 2018 Printed January 31, 2019
https://doi.org/10.4134/CKMS.c180044
Copyright © The Korean Mathematical Society.
On $3$-dimensional Lorentzian concircular structure manifolds
Sudhakar Kumar Chaubey, Absos Ali Shaikh
Shinas College of Technology, University of Burdwan
The aim of the present paper is to study the Eisenhart problems of finding the properties of second order parallel tensors (symmetric and skew-symmetric) on a $3$-dimensional $LCS$-manifold. We also investigate the properties of Ricci solitons, Ricci semisymmetric, locally $\phi$-symmetric, $\eta$-parallel Ricci tensor and a non-null concircular vector field on $(LCS)_3$-manifolds.
Keywords: $(LCS)_3$-manifolds, symmetric spaces, concircular vector field, second order parallel tensors, $\eta$-parallel Ricci tensor and Ricci solitons
MSC numbers: Primary 53C10, 53C25, 53C40
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