On Complex $η $-Einstein Normal Complex Contact Metric Manifolds - Turgut Vanli, Aysel -; Unal, Inan - (Communications in Mathematics and Applications, 2017)
The aim of this paper is focusing on $η$-Einstein geometry of complex contact metric manifolds. We give the definition of complex $η$-Einstein normal complex contact metric manifolds. In addition, we study on Weyl conformal curvature tensor $\mathcal{W}$ and concircular curvature tensor $\mathcal{Z}$ and we show that a normal complex contact metric manifold which satisfy $\mathcal{Z}\left( U,X\right) .\mathcal{W}=0$ and $\mathcal{Z}\left( V,X\right). \mathcal{W}=0$ complex $η$-Einstein. Also, we prove that a projectively semi-symmetric normal complex contact metric manifold is complex $η$-Einstein.