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Journal of Lie Theory 20 (2010), No. 4, 665--672
Copyright Heldermann Verlag 2010

A Lie-Trotter Formula for Riemannian Manifolds and Applications

Jimmie Lawson
Dept. of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A.

Yongdo Lim
Dept. of Mathematics, Kyungpook National University, Taegu 702-701, South Korea

We derive a Lie-Trotter formula for general Riemannian manifolds based on the local existence of a midpoint operation and given in terms of that operation. As a corollary one obtains that continuous maps between Riemannian manifolds that preserve the local midpoint structure are smooth. In particular, this is true for (local) isometries.

Keywords: Riemannian geometry, Lie-Trotter fomula, midpoints, differentiability.

MSC: 53C20

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