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 W and concircular curvature tensor Z and we show that a normal complex contact metric manifold which satisfy Z( U,X) .W=0 and Z( V,X). W=0 complex η-Einstein. Also, we prove that a projectively semi-symmetric normal complex contact metric manifold is complex η-Einstein.