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VOL. 14 | 2013 Some Remarks on the Exponential Map on the Groups SO(n) and SE(n)
Ramona-Andreea Rohan

Editor(s) Ivaïlo M. Mladenov, Andrei Ludu, Akira Yoshioka


The problem of describing or determining the image of the exponential map $ \exp :\mathfrak{g}\rightarrow G$ of a Lie group $G$ is important and it has many applications. If the group $G$ is compact, then it is well-known that the exponential map is surjective, hence the exponential image is $G$. In this case the problem is reduced to the computation of the exponential and the formulas strongly depend on the group $G$. In this paper we discuss the generalization of Rodrigues formulas for computing the exponential map of the special orthogonal group ${\rm SO}(n) $, which is compact, and of the special Euclidean group ${\rm SE}(n)$, which is not compact but its exponential map is surjective, in the case $ n\geq 4$.


Published: 1 January 2013
First available in Project Euclid: 13 July 2015

zbMATH: 1382.22015
MathSciNet: MR3183938

Digital Object Identifier: 10.7546/giq-14-2013-160-175

Rights: Copyright © 2013 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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