On ϕ-Ricci symmetric N(k)-contact metric manifolds

Sudipta Biswas; Avik De

doi:10.55937/sut/1266409166

June 2009 On

\phi

-Ricci symmetric

N(k)

-contact metric manifolds

Sudipta Biswas, Avik De

Author Affiliations +

SUT J. Math. 45(2): 167-176 (June 2009). DOI: 10.55937/sut/1266409166

Abstract

The object of the present paper is to study $\phi$ -Ricci symmetric $N(k)$ -contact metric manifolds and $\phi$ -Ricci symmetric $N(k)$ -contact metric manifolds of dimension three. It is proved that a $\phi$ -Ricci symmetric $N(k)$ -contact metric manifold ${M^{2n + 1}}(n > 1)$ is Sasakian. Next we prove that a three dimensional $N(k)$ -contact metric manifold is locally $\phi$ -Ricci symmetric if and only if the scalar curvature is constant. Finally we give examples of $\phi$ -Ricci symmetric $N(k)$ -contact metric manifolds.

Acknowledgement

The authors are thankful to the referee for his/her valuable suggestions in the improvement of the paper.

Citation

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Sudipta Biswas. Avik De. "On $\phi$ -Ricci symmetric $N(k)$ -contact metric manifolds." SUT J. Math. 45 (2) 167 - 176, June 2009. https://doi.org/10.55937/sut/1266409166