On the concircular curvature of a $(\kappa, \mu, \nu)$-manifold

Florence Gouli-Andreou and Evaggelia Moutafi

Vol. 269 (2014), No. 1, 113–132

DOI: 10.2140/pjm.2014.269.113

Abstract

We study ($\kappa ,\mu ,\nu$)-contact metric 3-manifolds (a notion introduced by Koufogiorgos, Markellos and Papantoniou) that are Ricci flat, or are Einstein but not Sasakian, or satisfy $\nabla Z=0$, where $Z$ is the concircular curvature tensor, or satisfy $Z\left(\xi ,X\right)\cdot Z=0$, where $\xi$ is the Reeb field, or satisfy $Z\left(\xi ,X\right)\cdot S=0$, where $S$ is the Ricci tensor, or finally satisfy $R\left(\xi ,X\right)\cdot Z=0$, where $R$ is the Riemannian curvature tensor.

Keywords

contact metric manifold, $(\kappa, \mu, \nu)$-contact metric manifolds, $\eta$-Einstein, Ricci flat, Sasakian manifold, concircular curvature tensor, pseudosymmetric manifold

Mathematical Subject Classification 2010

Primary: 53C15, 53C25, 53D10

Secondary: 53C35

Milestones

Received: 15 November 2012

Revised: 19 December 2012

Accepted: 2 January 2013

Published: 15 July 2014