Hodge decomposition theorem on compact $d$-K\"ahler manifolds

Sanjay Amrutiya; Ayush Jaiswal

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arXiv · 2406.09312

Hodge decomposition theorem on compact $d$-K\"ahler manifolds

Sanjay Amrutiya·Ayush Jaiswal

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Abstract

In 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\"ahler 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\"ahler manifolds, which establishes a crucial relationship between certain de-Rham cohomology groups and Dolbeault cohomology groups on a compact $d$-K\"ahler manifold .

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BibTeX RIS

Sanjay Amrutiya, Ayush Jaiswal. 2024-06-13. Hodge decomposition theorem on compact $d$-K\"ahler manifolds. https://arxiv.org/abs/2406.09312

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