Weighted diffeomorphism groups of Riemannian manifolds |
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Institution: | Department of Mathematics and Statistics, University of Vaasa, P.O. Box 700, 65101 Vaasa, Finland, |
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Abstract: | In this paper, we define locally convex vector spaces of weighted vector fields and use them as model spaces for Lie groups of weighted diffeomorphisms on Riemannian manifolds. We prove an easy condition on the weights that ensures that these groups contain the compactly supported diffeomorphisms. We finally show that for the special case where the manifold is the euclidean space, these Lie groups coincide with the ones constructed in the author’s earlier work (Walter, 2012). |
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Keywords: | Infinite-dimensional Lie group Diffeomorphism group Riemannian manifold Weighted vector fields Weighted function space |
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