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A three-manifold is a space that locally looks like Euclidean three-dimensional space
6
votes
2
answers
536
views
Do geodesics in SL2R map to geodesics in the hyperbolic plane?
I am looking for a reference/proof/disproof of the following statement.
Equip the Lie group $SL_2(\mathbb{R})$ with the left-invariant Riemannian metric, whichis given on the Lie algebra by $\langle …
26
votes
7
answers
2k
views
Tetrahedra with prescribed face angles
I am looking for an analogue for the following 2 dimensional fact:
Given 3 angles $\alpha,\beta,\gamma\in (0;\pi)$ there is always a triangle with these prescribed angles. It is spherical/euclidean/h …