Article ID Journal Published Year Pages File Type
4605902 Differential Geometry and its Applications 2015 9 Pages PDF
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
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