%0 Journal Article
%T On three-dimensional $N(k)$-paracontact metric manifolds and Ricci solitons
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A De, U.C.
%A Deshmukh, S.
%A Mandal, K.
%D 2017
%\ 11/30/2017
%V 43
%N 6
%P 1571-1583
%! On three-dimensional $N(k)$-paracontact metric manifolds and Ricci solitons
%K Ricci semisymmetric
%K cyclic parallel Ricci tensor
%K $\eta$-parallel Ricci tensor
%K Ricci soliton
%K Einstein manifold
%R
%X 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.
%U http://bims.iranjournals.ir/article_1040_a446023e2cc7956949c8c04a16793c63.pdf