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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 …
HenrikRüping's user avatar
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 …
HenrikRüping's user avatar