# Tagged Questions

**2**

votes

**0**answers

62 views

### Are there a group of mappings from (n-1)-dim space to an (n-1)-sphere guaranteeing the orthogonality of images?

Hello, everyone.
As we know that in an $n$-dimensional Euclidean space $\mathbb{R}^n$, there exists a continuous bijective mapping from a subset $V^{n-1}\subseteq\mathbb{R}^{n-1}$ to a unit ...

**1**

vote

**0**answers

111 views

### What is the intrinsic geometry of a feasible set?

In constraint optimization problem, one is often confronted with the following problem:
$min$ $f(x)$ , $x \in R^n$
given
$g_i(x) = c_i$ where $i = 1,...m$
$h_j(x) < c_j$ where $j = 1,...p$
...

**5**

votes

**2**answers

560 views

### Pursuit-Evasion on a Manifold

I know pursuit-evasion has been studied in many contexts, including
on a manifold (e.g., Melikyan,
"Geometry of Pursuit-Evasion Games on Two-Dimensional Manifolds"),
but I have not seen this version:
...

**12**

votes

**3**answers

2k views

### What is the difference between holonomy and monodromy?

And what is the simplest example in which one is trivial and the other is not?

**5**

votes

**0**answers

467 views

### Homometric $\Rightarrow$ isometric?

Suppose you know that there is a mapping between
two Riemmanian manifolds $M_1$ and $M_2$ such that,
for each $x_1 \in M_1$, the (codimension-1) measure of the set of points
at distance $d$ from $x_1$ ...

**15**

votes

**2**answers

1k views

### A book on locally ringed spaces?

Are there enough interesting results that hold for general locally ringed spaces for a book to have been written? If there are, do you know of a book? If you do, pelase post it, one per answer and a ...