# Tagged Questions

**0**

votes

**0**answers

49 views

### How to prove that the definition of saddle surface is affine invariant? [migrated]

I have a smooth saddle surface in $\mathbb{R}^n$, so for any normal vector the second fundamental form of the surface has $\det \leq 0$. How can I proove that the surface is still saddle if I stretch ...

**3**

votes

**1**answer

100 views

### Symmetry group for the frame bundle of a G-space

Let $Q$ be a smooth manifold, and let $G$ be a Lie group which acts smoothly on $Q$ on the left.
Question 1: does the group $G$ act naturally on the tangent bundle $TQ \to Q$?
My motivation here ...

**10**

votes

**2**answers

455 views

### Helix translates as geodesics

I believe one can fill $\mathbb{R}^3$ with
horizontal translates of the helix
$(\cos t, \sin t, t) \;,\; t \in \mathbb{R}$,
so that every point of $\mathbb{R}^3$
lies in exactly one helix.
I am ...