@article {
author = {De, U.C. and Deshmukh, S. and Mandal, K.},
title = {On three-dimensional $N(k)$-paracontact metric manifolds and Ricci solitons},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {43},
number = {6},
pages = {1571-1583},
year = {2017},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {The aim of this paper is to characterize $3$-dimensional $N(k)$-paracontact metric manifolds satisfying certain curvature conditions. We prove that a $3$-dimensional $N(k)$-paracontact metric manifold $M$ admits a Ricci soliton whose potential vector field is the Reeb vector field $xi$ if and only if the manifold is a paraSasaki-Einstein manifold. Several consequences of this result are discussed. Finally, an illustrative example is constructed.},
keywords = {Ricci semisymmetric,cyclic parallel Ricci tensor,$\eta$-parallel Ricci tensor,Ricci soliton,Einstein manifold},
url = {http://bims.iranjournals.ir/article_1040.html},
eprint = {http://bims.iranjournals.ir/article_1040_a446023e2cc7956949c8c04a16793c63.pdf}
}