The Levi-Civita connection and Chern connections for cocycle deformations of Kähler manifolds
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910025112354816 |
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| author | Bhowmick, Jyotishman Ghosh, Bappa |
| author_facet | Bhowmick, Jyotishman Ghosh, Bappa |
| contents | 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 Kähler 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03340 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Levi-Civita connection and Chern connections for cocycle deformations of Kähler manifolds Bhowmick, Jyotishman Ghosh, Bappa Quantum Algebra Mathematical Physics Operator Algebras 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 Kähler 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. |
| title | The Levi-Civita connection and Chern connections for cocycle deformations of Kähler manifolds |
| topic | Quantum Algebra Mathematical Physics Operator Algebras |
| url | https://arxiv.org/abs/2504.03340 |