Some properties of the locally conformal Kähler manifold

Mileva Prvanović

We determine the holomorphic curvature tensor of locally conformal Kähler manifold and find the expression of the Riemannian curvature tensor of such manifold if it is of pointwise constant holomorphic sectional curvature. We examine the geodesic mapping using the holomorphic curvature tensor and apply the obtained results to the locally conformal Kähler manifolds.