Geodesic
Ricci solitons and gradient Ricci solitons on $N(k)$-paracontact manifolds
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 15 (2019) no. 3, pp. 307-320 Cet article a éte moissonné depuis la source Math-Net.Ru

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An $\eta$-Einstein paracontact manifold $M$ admits a Ricci soliton $(g,\xi)$ if and only if $M$ is a $K$-paracontact Einstein manifold provided one of the associated scalars $\alpha$ or $\beta$ is constant. Also we prove the non-existence of Ricci soliton in an $N(k)$-paracontact metric manifold $M$ whose potential vector field is the Reeb vector field $\xi$. Moreover, if the metric $g$ of an $N(k)$-paracontact metric manifold $M^{2n+1}$ is a gradient Ricci soliton, then either the manifold is locally isometric to a product of a flat $(n+1)$-dimensional manifold and an $n$-dimensional manifold of negative constant curvature equal to $-4$, or $M^{2n+1}$ is an Einstein manifold. Finally, an illustrative example is given. 
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     title = {Ricci solitons and gradient {Ricci} solitons on $N(k)$-paracontact manifolds},
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     url = {http://geodesic.mathdoc.fr/item/JMAG_2019_15_3_a0/}
}
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Uday Chand De; Krishanu Mandal. Ricci solitons and gradient Ricci solitons on $N(k)$-paracontact manifolds. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 15 (2019) no. 3, pp. 307-320. http://geodesic.mathdoc.fr/item/JMAG_2019_15_3_a0/

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