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Results tagged with dg.differential-geometry
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user 25511
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
22
votes
2
answers
3k
views
Flows of vector fields and diffeomorphisms isotopic to the identity
Let $M$ be a compact manifold and $\varphi : M \longrightarrow M$ be a diffeomorphism which is isotopic to the identity. Does there exist a vector field $ X $ on $M$ such that $\varphi$ is the flow at …
- 2,696
2
votes
0
answers
242
views
Variations of the mean curvature
Good evening everyone,
I am facing a technical problem, maybe one of you can help.
Given a spacelike surface $S$ with mean curvature 0 in a lorentzian $3$-manifold with constant sectionnal curvature …
- 2,696
1
vote
1
answer
119
views
Surfaces of $\mathbb{R}^3$ invariant by an affine map
I have a rather elementary question.
I would like to know what are the surfaces of $\mathbb{R}^3$ which are globally preserved by the action of a linear or affine map in a non trivial way. This quest …
- 2,696
8
votes
3
answers
265
views
Zone of negative curvature on surfaces embedded in $\mathbb{R}^3$
I consider the standard embedding of a compact oriented surface $\Sigma$ (say of genus 2) in the Euclidean space $\mathbb{R}^3$. I have coloured on the picture below the zone of this surface where the …
- 2,696
4
votes
2
answers
265
views
Metrics with fixed conformal structure and diameter
I have three questions.
I consider a sequence of metrics $h_n$ on a two-dimensional torus which all induce the same conformal structure. Suppose that the volume of $h_n$ is always $1$. Is it possibl …
- 2,696