Journal of Lie Theory

no. 4
A Lie-Trotter Formula for Riemannian Manifolds and Applications
Journal of Lie Theory, Volume 20 (2010) no. 4, pp. 665-672
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.
DOI: 10.5802/jolt.613
Classification: 53C20
Keywords: Riemannian geometry, Lie-Trotter fomula, midpoints, differentiability 
@article{JOLT_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},
     year = {2010},
     volume = {20},
     number = {4},
     doi = {10.5802/jolt.613},
     zbl = {1213.53048},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.613/}
}
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J. Lawson; Y. Lim. A Lie-Trotter Formula for Riemannian Manifolds and Applications. Journal of Lie Theory, Volume 20 (2010) no. 4, pp. 665-672. doi: 10.5802/jolt.613

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