DECOMPOSABLE ON KAEHLERIAN MANIFOLDS OF CONFORMAL RECURRENT CURVATURE TENSOR

Abstract

Adati and Miyazawa (1967), have studied on a Riemannian space with recurrent conformally curvature and Deszcz (1976), has studied on semi-composable conformally recurrent and conformally birecurrent Riemannian spaces. After then, Negi (2017) have calculated Theorems on almost product and decomposable spaces. In this paper, we define and study decomposition on Kaehlerian manifolds of conformal recurrent curvature tensor and some theorems are established. Also, we have proved that if a Kaehlerian manifold $k_{n}$ of recurrent conformal curvature is decomposable then the decomposition space $\Omega_{n-r}$ is Einstein and if a Kaehlerian conformally recurrent manifold $k_{n}$ is decomposable then the recurrence vector is a gradient or the decomposition space $\Omega_{r}$ has constant curvature.