Geodesic
A Lie-Trotter Formula for Riemannian Manifolds and Applications
Journal of Lie theory, Tome 20 (2010) no. 4, pp. 665-672.

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 53C20
Mots-clés : Riemannian geometry, Lie-Trotter fomula, midpoints, differentiability 
@article{JLT_2010_20_4_JLT_2010_20_4_a2,
     author = {J. Lawson and Y. Lim },
     title = {A {Lie-Trotter} {Formula} for {Riemannian} {Manifolds} and {Applications}},
     journal = {Journal of Lie theory},
     pages = {665--672},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2010},
     url = {http://geodesic.mathdoc.fr/item/JLT_2010_20_4_JLT_2010_20_4_a2/}
}
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J. Lawson; Y. Lim . A Lie-Trotter Formula for Riemannian Manifolds and Applications. Journal of Lie theory, Tome 20 (2010) no. 4, pp. 665-672. http://geodesic.mathdoc.fr/item/JLT_2010_20_4_JLT_2010_20_4_a2/