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arXiv · 2504.03340

The Levi-Civita connection and Chern connections for cocycle deformations of K\"{a}hler manifolds

Jyotishman Bhowmick·Bappa Ghosh
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Abstract

We consider unitary cocycle deformations of covariant $\ast$-differential calculi. We prove that complex structures, holomorphic bimodules and Chern connections on the deformed calculus are twists of their untwisted counterparts. Moreover, for cocycle deformations of a class of classical K\"ahler manifolds, the Levi-Civita connection on the space of one-forms of the deformed calculus is shown to be a direct sum of the Chern connections on the twisted holomorphic and the anti-holomorphic bimodules. Our class of examples also includes cocycle deformations of the Heckenberger-Kolb calculi.

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BibTeXRIS

Jyotishman Bhowmick, Bappa Ghosh. 2025-04-04. The Levi-Civita connection and Chern connections for cocycle deformations of K\"{a}hler manifolds. https://arxiv.org/abs/2504.03340

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