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A reduced parallel transport equation on Lie Groups with a left-invariant metric

Abstract : This paper presents a derivation of the parallel transport equation expressed in the Lie algebra of a Lie group endowed with a left-invariant metric. The use of this equation is exemplified on the group of rigid body motions SE(3), using basic numerical integration schemes, and compared to the pole ladder algorithm. This results in a stable and efficient implementation of parallel transport. The implementation leverages the python package geomstats and is available online.
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https://hal.inria.fr/hal-03154318
Contributor : Nicolas Guigui <>
Submitted on : Tuesday, March 2, 2021 - 10:35:43 AM
Last modification on : Friday, July 9, 2021 - 2:08:56 PM

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Nicolas Guigui, Xavier Pennec. A reduced parallel transport equation on Lie Groups with a left-invariant metric. GSI 2021 - 5th conference on Geometric Science of Information, Jul 2021, Paris, France. pp.119-126, ⟨10.1007/978-3-030-80209-7_14⟩. ⟨hal-03154318v2⟩

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