2
votes
0answers
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
0answers
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
2answers
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
3answers
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
0answers
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
2answers
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 ...