Exponential map
The exponential map in the context of Lie groups is exp:G→G, or equivalently exp:g→G. We continue with discussion of the Lie group
R.
The exponential of a tangent vector {,
,
}∈
G is determined by the integral curve of the left-invariant vector field induced by v through e∈G. Recall the general form of a left-invariant vector field on G.
Even for "simple" instances for v∈G, Mathematica has trouble finding exact solutions. We try the three basis vectors
,
,
of g.
For we yield the (unique) solution exp t
={1,t,0}, since
Created by Mathematica (September 30, 2006) | ![]() |