Some notes on metallic Kähler manifolds


Aydin Gezer, Fatih Topcuoglu, Uday Chand De




The present paper deals with metallic Kähler manifolds. Firstly, we define a tensor H which can be written in terms of the (0, 4)−Riemannian curvature tensor and the fundamental 2−form of a metallic Kähler manifold and study its properties and some hybrid tensors. Secondly, we obtain the conditions under which a metallic Hermitian manifold is conformal to a metallic Kähler manifold. Thirdly, we prove that the conformal recurrency of a metallic Kähler manifold implies its recurrency and also obtain the Riemannian curvature tensor form of a conformally recurrent metallic Kähler manifold with non-zero scalar curvature. Finally, we present a result related to the notion of Z recurrent form on a metallic Kähler manifold.