Lines on holomorphic contact manifolds and a generalization of $(2,3,5)$-distributions to higher dimensions

Jun-Muk Hwang; Qifeng Li

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arXiv · 2301.12622

Lines on holomorphic contact manifolds and a generalization of $(2,3,5)$-distributions to higher dimensions

Jun-Muk Hwang·Qifeng Li

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Abstract

Since the celebrated work by Cartan, distributions with \nobreak{small} growth vector $(2,3,5)$ have been studied extensively. In the holomorphic setting, there is a natural correspondence between holomorphic $(2,3,5)$-distributions and nondegenerate lines on holomorphic contact manifolds of dimension 5. We generalize this correspondence to higher dimensions by studying nondegenerate lines on holomorphic contact manifolds and the corresponding class of distributions of small growth vector $(2m, 3m, 3m+2)$ for any positive integer $m$.

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Jun-Muk Hwang, Qifeng Li. 2023-01-30. Lines on holomorphic contact manifolds and a generalization of $(2,3,5)$-distributions to higher dimensions. https://arxiv.org/abs/2301.12622

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