Exponential maps of Sobolev metrics on loop groups

Misiołek, Gerard

doi:10.1090/S0002-9939-99-05063-7

Exponential maps of Sobolev metrics on loop groups
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Proc. Amer. Math. Soc. 127 (1999), 2475-2482 Request permission

Abstract:

We find conditions for the exponential map on a weak riemannian Hilbert manifold to be a nonlinear Fredholm map of index zero and apply the result to left-invariant Sobolev metrics on loop groups.

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