3
votes
0answers
183 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 ...
14
votes
1answer
592 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 ...
23
votes
4answers
2k 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 ...
22
votes
11answers
4k 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 ...
38
votes
7answers
4k 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 ...
5
votes
1answer
653 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 ...