# Tagged Questions

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### 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 ...
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### What is the intrinsic geometry of a feasible set? [on hold]

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 $j = 1,...p$ ...
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### 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: ...
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### What is the difference between holonomy and monodromy?

And what is the simplest example in which one is trivial and the other is not?
### 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 $x_1$ ...