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 \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.
Löwe, H., Wu, Y., Carricato, M. (2016). Symmetric subspaces of SE(3). ADVANCES IN GEOMETRY, 16(3), 381-388 [10.1515/advgeom-2016-0015].
Symmetric subspaces of SE(3)
WU, YUANQING;CARRICATO, MARCO
2016
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 \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.File in questo prodotto:
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