The Ricci curvature of finite dimensional approximations to loop and path groups |
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Authors: | Matthew Cecil |
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Affiliation: | Department of Mathematics, University of Connecticut, Storrs, CT 06269, USA |
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Abstract: | Let W(G) and L(G) denote the path and loop groups respectively of a connected real unimodular Lie group G endowed with a left-invariant Riemannian metric. We study the Ricci curvature of certain finite dimensional approximations to these groups based on partitions of the interval [0,1]. We find that the Ricci curvatures of the finite dimensional approximations are bounded below independent of partition iff G is of compact type with an Ad-invariant metric. |
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Keywords: | 46T10 58D15 22E65 |
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