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Geometry of the contactomorphism group | | Boramey Chhay
; Stephen C. Preston
; | | Date: |
10 Jan 2015 | | 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 $mathcal{D}_ heta(M)$ 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. | | Source: | arXiv, 1501.2292 | | Services: | Forum | Review | PDF | Favorites | |
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