Amrutiya, SanjaySanjayAmrutiyaJaiswal, AyushAyushJaiswal2025-08-282025-08-282024-06-01http://arxiv.org/abs/2406.09312https://d8.irins.org/handle/IITG2025/20170In this article, we will explore the fundamental concepts, including various basic concepts on d-complex manifolds, along with several differential operators and examine the relationships between them. A d-K�hler manifold is a d-complex manifold equipped with a metric that satisfies a specific condition. We prove the Hodge decomposition theorem on compact d-K�hler manifolds, which establishes a crucial relationship between certain de-Rham cohomology groups and Dolbeault cohomology groups on a compact d-K�hler manifolden-USe-Printe-Print123456789/555