
Journal of Lie Theory 20 (2010), No. 4, 665672 Copyright Heldermann Verlag 2010 A LieTrotter Formula for Riemannian Manifolds and Applications Jimmie Lawson Dept. of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A. lawson@math.lsu.edu Yongdo Lim Dept. of Mathematics, Kyungpook National University, Taegu 702701, South Korea ylim@knu.ac.kr We derive a LieTrotter 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, LieTrotter fomula, midpoints, differentiability. MSC: 53C20 [ Fulltextpdf (141 KB)] for subscribers only. 