On three-dimensional $N(k)$-paracontact metric manifolds and Ricci solitons

De, U.C.; Deshmukh, S.; Mandal, K.

On three-dimensional $N(k)$-paracontact metric manifolds and Ricci solitons

Document Type : Research Paper

Authors

¹ Department of Pure Mathematics‎, ‎University of Calcutta‎, ‎35‎, ‎Ballygunge Circular Road‎, ‎Kol‎- ‎700019‎, ‎West Bengal‎, ‎India.

² Department of Mathematics‎, ‎College of Science‎, ‎King saud University‎, ‎P.O‎. ‎Box-2455‎, ‎Riyadh-11451‎, ‎Saudi Arabia.

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

Main Subjects

53-XX Differential geometry

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