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arXiv · 2410.15402

Born geometry via K\"unneth structures and recursion operators

M. J. D. Hamilton·D. Kotschick·P. N. Pilatus
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Abstract

We propose a simple definition of a Born geometry in the framework of K\"unneth 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 K\"unneth connection. We also give examples of integrable Born geometries on nilmanifolds.

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BibTeXRIS

M. J. D. Hamilton, D. Kotschick, P. N. Pilatus. 2024-10-20. Born geometry via K\"unneth structures and recursion operators. https://doi.org/10.1007/s00220-025-05296-4

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