On three-dimensional $N(k)$-paracontact metric manifolds and Ricci solitons
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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.
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Journal title
volume 43 issue 6
pages 1571- 1583
publication date 2017-11-30
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