An Introduction to Calabi-Yau Manifolds
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912214669066240 |
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| author | Patterson, Aidan |
| author_facet | Patterson, Aidan |
| contents | The goal of this paper is to develop the theory of Courant algebroids with integrable para-Hermitian vector bundle structures by invoking the theory of Lie bialgebroids. We consider the case where the underlying manifold has an almost para-complex structure, and use this to define a notion of para-holomorphic algebroid. We investigate connections on para-holomorphic algebroids and determine an appropriate sense in which they can be para-complex. Finally, we show through a series of examples how the theory of exact para-holomorphic algebroids with a para-complex connection is a generalization of both para-Kähler geometry and the theory of Poisson-Lie groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00167 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Introduction to Calabi-Yau Manifolds Patterson, Aidan Differential Geometry Symplectic Geometry The goal of this paper is to develop the theory of Courant algebroids with integrable para-Hermitian vector bundle structures by invoking the theory of Lie bialgebroids. We consider the case where the underlying manifold has an almost para-complex structure, and use this to define a notion of para-holomorphic algebroid. We investigate connections on para-holomorphic algebroids and determine an appropriate sense in which they can be para-complex. Finally, we show through a series of examples how the theory of exact para-holomorphic algebroids with a para-complex connection is a generalization of both para-Kähler geometry and the theory of Poisson-Lie groups. |
| title | An Introduction to Calabi-Yau Manifolds |
| topic | Differential Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2502.00167 |