Nilpotent structures of oriented neutral vector bundles
Abstract
In this paper, we study nilpotent structures of an oriented vector bundle $E$ of rank $4n$ with a neutral metric $h$ and an $h$-connection $\nabla$. We define $H$-nilpotent structures of $(E, h, \nabla )$ for a Lie subgroup $H$ of $SO(2n, 2n)$ related to neutral hyperKähler structures. We observe that there exist a complex structure $I$ and paracomplex structures $J_1$, $J_2$ of $E$ such that $h$, $\nabla$, $I$, $J_1$, $J_2$ form a neutral hyperKähler structure of $E$ if and only if there exists an $H$-nilpotent structure of $(E, h, \nabla )$.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2024
- DOI:
- 10.48550/arXiv.2405.05003
- arXiv:
- arXiv:2405.05003
- Bibcode:
- 2024arXiv240505003A
- Keywords:
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- Mathematics - Differential Geometry