## Proceedings of the International Conference on Geometry, Integrability and Quantization

### Some Remarks on the Exponential Map on the Groups SO(n) and SE(n)

Ramona-Andreea Rohan

#### Abstract

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 $n\geq 4$.

#### Article information

Dates
First available in Project Euclid: 13 July 2015

https://projecteuclid.org/ euclid.pgiq/1436795020

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

Mathematical Reviews number (MathSciNet)
MR3183938

Zentralblatt MATH identifier
1382.22015

#### Citation

Rohan, Ramona-Andreea. Some Remarks on the Exponential Map on the Groups SO(n) and SE(n). Proceedings of the Fourteenth International Conference on Geometry, Integrability and Quantization, 160--175, Avangard Prima, Sofia, Bulgaria, 2013. doi:10.7546/giq-14-2013-160-175. https://projecteuclid.org/euclid.pgiq/1436795020