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## Main Question or Discussion Point

Hello,

Let's suppose that I have a Lie group G parametrized by one real scalar

Is it generally correct to say that the

If so, how can I prove this statement?

Thanks.

Let's suppose that I have a Lie group G parametrized by one real scalar

*t*and acting on ℝ^{2}.Is it generally correct to say that the

*orbits*of the points of ℝ^{2}under the group action are one-dimensional submanifolds of ℝ^{2}, because G is parametrized by one single scalar?If so, how can I prove this statement?

Thanks.