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LINES ON HOLOMORPHIC CONTACT MANIFOLDS AND A GENERALIZATION OF $(2,3,5)$-DISTRIBUTIONS TO HIGHER DIMENSIONS

Part of: General theory of differentiable manifolds Complex manifolds

Published online by Cambridge University Press:  23 February 2023

JUN-MUK HWANG Open the ORCID record for JUN-MUK HWANG [Opens in a new window]  and
QIFENG LI Open the ORCID record for QIFENG LI [Opens in a new window]
JUN-MUK HWANG*
Affiliation:
Center for Complex Geometry Institute for Basic Science (IBS) Daejeon 34126 Republic of Korea
QIFENG LI
Affiliation:
School of Mathematics Shandong University Jinan 250100 China qifengli@sdu.edu.cn
*
jmhwang@ibs.re.kr
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Abstract

Since the celebrated work by Cartan, distributions with 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.

MSC classification

Primary: 58A30: Vector distributions (subbundles of the tangent bundles)
Secondary: 32Q99: None of the above, but in this section
Type
Article
Information
Nagoya Mathematical Journal , Volume 251 , September 2023 , pp. 652 - 668
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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Footnotes

Hwang was supported by the Institute for Basic Science (IBS-R032-D1). Li was supported by the National Natural Science Foundation of China (Grant No. 12201348).

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