Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4605902 | Differential Geometry and its Applications | 2015 | 9 Pages |
Abstract
In this paper we examine the Riemannian geometry of the group of contactomorphisms of a compact contact manifold. We compute the sectional curvature of Dθ(M)Dθ(M) in the sections containing the Reeb field and show that it is non-negative. We also solve explicitly the Jacobi equation along the geodesic corresponding to the flow of the Reeb field and determine the conjugate points. Finally, we show that the Riemannian exponential map is a non-linear Fredholm map of index zero.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Boramey Chhay, Stephen C. Preston,