Abstract
Abstract Being 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 µ(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.
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