On the Geometry of the Kähler Golden Manifold

The main objective of this paper is to investigate the properties related to the sectional curvatures of a Kähler golden manifold, an almost Hermitian golden manifold whose almost complex golden structure is parallel with respect to the Levi–Civita connection. Under certain conditions, we prove that a Kähler golden manifold with constant sectional curvature is flat. We introduce the concepts of Φ-holomorphic sectional curvature and Φ-holomorphic bi-sectional curvature on a Kähler golden manifold, and compare them respectively with the holomorphic sectional curvature and holomorphic bi-sectional curvature on a Kähler manifold.