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Curves on a Plane

Mikhail Smilovic

出版	McGill University Libraries, 2011
URL	http://books.google.com.hk/books?id=RfgmnQEACAAJ&hl=&source=gbs_api

註釋

In this thesis, we study the space of immersions from the circle to the plane Imm(S1, R2), modulo the group of diffeomorphisms on S1. We discuss various Riemannian metrics and find surprisingly that the L2-metric fails to separate points. We show two methods of strengthening this metric, one to obtain a non-vanishing metric, and the other to stabilize the minimizing energy flow. We give the formulas for geodesics, energy and give an example of computed geodesics in the case of concentric circles. We then carry our results over to the larger spaces of immersions from a compact manifold M to a Riemannian manifold (N, g), modulo the group of diffeomorphisms on ...