Geometry of the contactomorphism group

2015/01/09 by Boramey Chhay, Chhay, Boramey, Stephen C. Preston +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1501.02292

9 pages

arxiv created 2015/01/09 · arxiv updated 2015/01/13

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 D_θ(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.

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