All Questions
Tagged with dg.differential-geometry examples
12 questions
73
votes
10
answers
11k
views
Riemannian surfaces with an explicit distance function?
I'm looking for explicit examples of Riemannian surfaces (two-dimensional Riemannian manifolds $(M,g)$) for which the distance function d(x,y) can be given explicitly in terms of local coordinates of ...
- 114k
46
votes
4
answers
10k
views
What are "good" examples of spin manifolds?
I'm trying to get a grasp on what it means for a manifold to be spin. My question is, roughly:
What are some "good" (in the sense of illustrating the concept) examples of manifolds which are spin (...
45
votes
13
answers
9k
views
Motivating the de Rham theorem
In grad school I learned the isomorphism between de Rham cohomology and singular cohomology from a course that used Warner's book Foundations of Differentiable Manifolds and Lie Groups. One thing ...
- 82.7k
28
votes
1
answer
2k
views
Example of 4-manifold with $\pi_1=\mathbb Q$
This might be well known for algebraic topologist. So I am looking for an explicit example of a 4 dimensional manifold with fundamental group isomorphic to the rationals $\mathbb Q$.
- 2,623
19
votes
1
answer
1k
views
What are "good" examples of string manifolds?
Based on this mathoverlow question, I would like to have a similar list for the case of string manifolds. An $n$-dim. Riemannian manifold $M$ is said to be string, if the classifying map of its bundle ...
8
votes
1
answer
1k
views
Example of a triangulable topological manifold which does not admit a PL structure
I know there are some examples of manifolds which don't admit a PL structure (combinatorial triangulation), and that it has been recently proven that in dimension $n\geq5$ there are manifold which are ...
- 683
8
votes
2
answers
1k
views
Example for an integral, rectifiable varifold with unbounded first variation
I'm just looking for an example of an integral, rectifiable varifold, which has no locally bounded first variation.
Recapitulation
for every $m$-rectifiable varifold $\mu$ exists a $m$-rectifiable ...
- 143
7
votes
0
answers
407
views
Linear vs smooth actions of finite groups on spheres, euclidean spaces and closed disks
I would like to know examples (with references, if possible) of the following:
(1) a finite group $G$ acting effectively and smoothly on a sphere $S^n$ (any $n$) but admitting no effective linear ...
6
votes
5
answers
2k
views
Examples of Riemannian Submersions
Is there any example of a Riemannian submersion, which is no fibration?
As far as I know, a (any) submersion is locally, but not globally, given by a fibration. The converse holds globally. ...
- 329
6
votes
1
answer
559
views
Example of a manifold with positive isotropic curvature but possibly negative Ricci curvature
Is there any example of a manifold with a positive isotropic curvature but it possibly obtains a negative Ricci curvature at some point and the direction? If we see the definition of the positive ...
- 123
4
votes
1
answer
340
views
Example of a specific manifold
I want to find a example of a manifold that has positive scalar curvature but is not half conformally flat.
Does there exists such manifolds?
Thanks.
- 371
3
votes
0
answers
271
views
Seek "typical examples" for the structure of spaces with two-sided Ricci bounds
By a 1990 paper of Michael Anderson, the following is true:
Theorem. Let the metric space $(X,d,p)$ be a pointed Gromov-Hausdorff limit of a sequence of complete pointed Riemannian manifolds $(M_i,...
- 3,212