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

Nicolas Guigui (1, 2) , Xavier Pennec (1, 2)

1 UniCA - Université Côte d'Azur
2 EPIONE - E-Patient : Images, données & mOdèles pour la médeciNe numériquE

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.

Domaines: Géométrie différentielle [math.DG]

Nicolas Guigui, Xavier Pennec. A reduced parallel transport equation on Lie Groups with a left-invariant metric. 2021. ⟨hal-03154318v1⟩