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Results tagged with dg.differential-geometry
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user 1227
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
12
votes
Accepted
Are limits of compact leaves compact?
Here's a counterexample where the foliation has codimension two. Consider the integral curves of a flow on the 3-torus $\mathbb{R}^3 \, / \,\mathbb{Z}^3$, defined by $x' = 0, y'=\cos 2\pi x, z'=\sin 2 …
- 6,486
13
votes
Accepted
Does the Baker-Campbell-Hausdorff formula hold for vector fields on a (compact) manifold?
To answer your first question, the composition of two time-1 flows won't necessarily be another time-1 flow.
One way to see this is to note that when a time-1 flow $\phi_X$ has a periodic point $P$ ( …
- 6,486
21
votes
Accepted
How large can you draw an island on a map?
Similar issues come up in studying gerrymandering (drawing political districts with partisan objectives), where it's useful to have a measure of how "irregular" a region is.
You can read about variou …
- 6,486
7
votes
Accepted
Relation between information geometry and geometric deep learning
The fields you're talking about are typically concerned with two different geometric spaces:
The space of input data to a neural network (geometric deep learning)
The parameter space of all neural ne …
- 6,486