Answer by Nick Alger for Meaning of Exponential map
The idea of an exponential is the continuous compounding of small actions. Suppose you start with an object $p$, perform an action on it $v$, and then add the result back to the original object. What...
View ArticleAnswer by Amitai Yuval for Meaning of Exponential map
Consider the following:Let $a\in\mathbb{R}$, and define a smooth vector field $X$ on $\mathbb{R}_+$, by $X(p)=ap$. Note that $X$ is left-invariant, when thinking of $\mathbb{R}_+$ as a Lie group. Now...
View ArticleMeaning of Exponential map
I've been studying differential geometry using Do Carmo's book. There's the notion of exponential map, but I don't understand why it is called "exponential" map. How does it has something to do with...
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