Symmetric subspaces of SE(3)

none3siPublished online: 27 Jun 2016Being a Lie group, the group SE(3) of orientation preserving motions of the real Euclidean 3-space becomes a symmetric space (in the sense of O. Loos) when endowed with the multiplication mu(g, h) = gh^{-1}g. In this note we classify all connected symmetric subspaces of SE(3) up to conjugation. Moreover, we indicate some of its important applications in robot kinematics.embargoed_20170627Löwe, Harald; Wu, Yuanqing; Carricato, MarcoLöwe, Harald; Wu, Yuanqing; Carricato, Marc