Legendrian cone structures and contact prolongations
Abstract
We study a cone structure ${\mathcal C} \subset {\mathbb P} D$ on a holomorphic contact manifold $(M, D \subset T_M)$ such that each fiber ${\mathcal C}_x \subset {\mathbb P} D_x$ is isomorphic to a Legendrian submanifold of fixed isomorphism type. By characterizing subadjoint varieties among Legendrian submanifolds in terms of contact prolongations, we prove that the canonical distribution on the associated contact Gstructure admits a holomorphic horizontal splitting.
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 DOI:
 10.48550/arXiv.2010.10818
 arXiv:
 arXiv:2010.10818
 Bibcode:
 2020arXiv201010818H
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Algebraic Geometry;
 53B99;
 14J45
 EPrint:
 14 pages, to appear in the proceedings volume of the Abel Symposium 2019