Legendrian cone structures and contact prolongations

2020/10/21 by Jun-Muk Hwang, Hwang, Jun-Muk
Mathematics · #14J45 #53B99 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2010.10818

openalex publication_date 2020/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a cone structure \mathcal C ⊂ \mathbb P D on a holomorphic contact manifold (M, D ⊂ T_M) such that each fiber \mathcal C_x ⊂ \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.

Citations

• Euler-symmetric projective varieties

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