Abstract
For loop groups (free and based), we compute the exact order of the curvature operator of the Levi-Civita connection depending on a Sobolev space parameter. This extends results of Freed (J Differ Geom 28:223–276, 1988) and Maeda et al. (Riemannian geometry on loop spaces. arXiv:0705.1008v3, 2008).
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Larraín-Hubach, A. The Order of Curvature Operators on Loop Groups. Lett Math Phys 89, 265–275 (2009). https://doi.org/10.1007/s11005-009-0352-1
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DOI: https://doi.org/10.1007/s11005-009-0352-1