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Results tagged with dg.differential-geometry
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user 117091
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
1
vote
1
answer
136
views
Global orthogonal coordinates on the open unit ball II
Original question here:
Global orthogonal coordinates on the open unit ball
So let $v_i:\mathbb{R}\to\text{Im }v_i\subset\mathbb{R}$ be diffeomorphisms, $1\leq i\leq n$, $\mathbb{R}^n=\mathbb{R}^{n_1 …
- 537
3
votes
0
answers
95
views
Tchebychev coordinates on hyperbolic space
Is there any known example of an open subset $U\subset\mathbb{H}^n$ with infinite volume admitting (global) Tchebychev coordinates for $n\geq3$?
- 537
6
votes
1
answer
235
views
Global orthogonal coordinates on the open unit ball
Is there any diffeomorphism $x:\mathbb{R}^n\to\text{Im }x=B_1\left(0\right)\subset\mathbb{R}^n$ such that
$x$ is an orthogonal chart, i.e., the coordinate vector fields $X_i=\partial x/\partial u_i …
- 537
8
votes
2
answers
469
views
Flat metric on compact surface minus a point
Let $T^2$ be a compact smooth surface and let $p\in T^2$. Suppose that $T^2$ admits a symmetric $\left(0,2\right)$-tensor which is a flat Riemannian metric restricted to $T^2-\{p\}$. Is it true that $ …
- 537