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 G-structure admits a holomorphic horizontal splitting.
- Publication:
-
arXiv e-prints
- 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
- E-Print:
- 14 pages, to appear in the proceedings volume of the Abel Symposium 2019