Born geometry via Künneth structures and recursion operators
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916758197108736 |
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| author | Hamilton, M. J. D. Kotschick, D. Pilatus, P. N. |
| author_facet | Hamilton, M. J. D. Kotschick, D. Pilatus, P. N. |
| contents | We propose a simple definition of a Born geometry in the framework of Künneth geometry. While superficially different, this new definition is equivalent to the known definitions in terms of para-quaternionic or generalized geometries. We discuss integrability of Born structures and their associated connections. In particular we find that for integrable Born geometries the Born connection is obtained by a simple averaging under a conjugation from the Künneth connection. We also give examples of integrable Born geometries on nilmanifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15402 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Born geometry via Künneth structures and recursion operators Hamilton, M. J. D. Kotschick, D. Pilatus, P. N. Differential Geometry Mathematical Physics Symplectic Geometry primary 53D05, 53C12, 53C15, secondary 53C55, 53D12, 81T30 We propose a simple definition of a Born geometry in the framework of Künneth geometry. While superficially different, this new definition is equivalent to the known definitions in terms of para-quaternionic or generalized geometries. We discuss integrability of Born structures and their associated connections. In particular we find that for integrable Born geometries the Born connection is obtained by a simple averaging under a conjugation from the Künneth connection. We also give examples of integrable Born geometries on nilmanifolds. |
| title | Born geometry via Künneth structures and recursion operators |
| topic | Differential Geometry Mathematical Physics Symplectic Geometry primary 53D05, 53C12, 53C15, secondary 53C55, 53D12, 81T30 |
| url | https://arxiv.org/abs/2410.15402 |