# Tagged Questions

**0**

votes

**1**answer

167 views

### relation with jacobifields in a small neighbourhood

hi,
I have the following question: Let $(M,g)$ be a complete Riemannian manifold with all sectional curvatures non-positive. Let $p \in M$ and consider the function $d(x)=dist_{g}(x,p)$ in a ...

**2**

votes

**2**answers

290 views

### Questions on calculating volume using n-1 forms

Is there an n-1 form on $R^n$ which calculates the volume of n-manifolds? Similarly, is there such a 1 form on $S^2$, and $RP^2$? I thought this has something to do with the orientation, is that ...

**3**

votes

**4**answers

1k views

### space of geodesics

hallo,
i have the following problem: Let $(M,g)$ be a compact Riemannian manifold with metric $g$ and $\nabla$ be the Levi-Civita Connection. Denote by $G(M) =${$\gamma: \mathbb{R} \rightarrow M | ...

**2**

votes

**0**answers

108 views

### isomap and self intersections

I sample a 2D surface in $\mathbb{R}^3$ with $N$ points, and compute an isomap using pairwise weighted geodesic distances. I am thus able to embed this surface into a $M$ dimensional space in which ...

**12**

votes

**3**answers

714 views

### orientations for zero-dimensional manifolds

I am teaching a course on manifolds, and soon I will have to prove the Stokes' theorem which, of course, involves defining oriented manifolds. There are many ways to define an oriented manifold. My ...

**3**

votes

**2**answers

243 views

### A local transitivity property of the automorphism group of a foliated manifold

Let $(M,\mathcal F)$ be a smooth foliated manifold. An automorphism of $(M,\mathcal F)$ is a diffeomorphism of $M$ that takes leaves of $\mathcal F$ onto leaves. Let now $L$ be a leaf of $\mathcal F$. ...