Characterization of Almost Complex Manifolds and Kähler Geometry

The primary objective of this task is to take steps an indicative immersion into the subject of complex geometry by providing several characterizations of Kähler manifolds. We have defined complex, Hermitian, almost complex and Kähler manifolds in this paper and studied some of their features. The main purpose of this article is with a view to understanding the complex, almost complex and Kähler manifolds and their relations with Lie brackets and affine connections. Finally, a theorem which is related to Kähler geometry is established. Dhaka Univ. J. Sci. 73(1): 39-42, 2025 (January)