Analyticity of Riemannian exponential maps on {rm Diff}(T)

T. Kappeler , E. Loubet , P. Topalov

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classification 🧮 math.DS math.AP

keywords exponentialmapsriemanniananalyticanalyticitychartcircledefines

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We study the exponential maps induced by Sobolev type right-invariant (weak) Riemannian metrics of order $k\ge1$ on the Lie group of smooth, orientation preserving diffeomorphisms of the circle. We prove that each of them defines an {\em analytic} Fr\'echet chart of the identity.

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Analyticity of Riemannian exponential maps on {rm Diff}(T)

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