# Tagged Questions

**5**

votes

**2**answers

1k views

### one-parameter subgroup and geodesics on Lie group

Hi,
Given a Matrix Lie Group, I would like to know if the one-parameter subgroups (which can be written as $\exp^{tX}$) are the same as the geodesics (locally distance minimizing curves). Geodesics ...

**5**

votes

**4**answers

824 views

### The Schwartz Space on a Manifold

I asked this question a couple of days ago on math.stackexchange, but have yet to receive a response, so I have decided to post this here.
This question is also vaguely related (both questions arose ...

**3**

votes

**1**answer

401 views

### Fixed points of the action of an algebraic group

Hello!
If a compact Lie group $K$ acts smoothly on a smooth manifold $M$, then the set $M^K$ of fixed points under this action is a smooth submanifold of $M$. This is proved for example in ...

**2**

votes

**3**answers

653 views

### analytic structure on lie groups

I need a reference for a result I have heard only very vaguely "A lie group (smooth) has a compatible analytic manifold structure".
(Would even appreciate a concise way to refer to the result..)
I ...

**1**

vote

**1**answer

381 views

### Understanding manifold GL+(3,R)/SO(3) ?

I'm trying to better understand the manifold GL+(3,R)/S0(3) which is diffeomorphic to positive definite symmetric matrices. My motivation is to understand U in F = RU where F in GL+(3,R) = deformation ...

**5**

votes

**2**answers

404 views

### Question on transversal slice of Lie group

Assume we have action of Lie group $G$ on a manifold $X$. Fix some orbit $\mathcal{O}$, it is known there exist transversal slice $S$ with respect to this orbit. Fix some point $x$ in $\mathcal{O}$, ...

**4**

votes

**2**answers

567 views

### Lie Semigroups?

Why is a Lie group wanted instead of a semigroup, what does the group structure give? References on this would be much appreciated.
I'm currently pondering manifolds and lie groups and their ...

**28**

votes

**3**answers

1k views

### What is the classifying space of “G-bundles with connections”

Let $G$ be a (maybe Lie) group, and $M$ a space (perhaps a manifold). Then a principal $G$-bundle over $M$ is a bundle $P \to M$ on which $G$ acts (by fiber-preserving maps), so that each fiber is a ...

**10**

votes

**3**answers

797 views

### Non-Lie Subgroups

A result of Borel and Lichnerowicz states that the holonomy group of a connection on a principal $G$-bundle is a Lie subgroup of $G$ (Cartan had earlier asserted this, but apparently without proof).
...