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.

14 pages, to appear in the proceedings volume of the Abel Symposium 2019

References in corpus (1)

• Euler-symmetric projective varieties