On Complex $\eta $-Einstein Normal Complex Contact Metric Manifolds
DOI:
https://doi.org/10.26713/cma.v8i3.509Keywords:
Normal complex contact metric manifold, conformal curvature tensor, concircular curvature tensor, projectively semi-symmetric, complex $\eta -$EinsteinAbstract
The aim of this paper is focusing on $\eta$-Einstein geometry of complex contact metric manifolds. We give the definition of complex $\eta$-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 $\eta$-Einstein. Also, we prove that a projectively semi-symmetric normal complex contact metric manifold is complex $\eta$-Einstein.
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