0
votes
0answers
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
1answer
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
2answers
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 ...