Contactomorphisms with L² metric on stream functions

2015/06/26 by Boramey Chhay, Chhay, Boramey
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1506.08178

arxiv created 2015/06/26 · openalex publication_date 2015/06/26 · arxiv updated 2015/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Here we investigate some geometric properties of the contactomorphism group D_θ(M) of a compact contact manifold with the L² metric on the stream functions. Viewing this group as a generalization to the D(S¹), the diffeomorphism group of the circle, we show that its sectional curvature is always non-negative and that the the Riemannian exponential map is not locally C¹. Lastly, we show that the quantomorphism group is a totally geodesic submanifold of D_θ(M) and talk about its Riemannian submersion onto the symplectomorphism group of the Boothby-Wang quotient of M.

Related

• Geometry of the contactomorphism group
• Riemannian geometry on the quantomorphism group
• Riemannian geometry of the contactomorphism group
• Geodesics of norms on the contactomorphisms group of ℝ²ⁿ × S¹
• The Group of Contact Diffeomorphisms for Compact Contact Manifolds