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Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
3
votes
De Rham decomposition theorem, generalisations and good references
Response to the first question:
Pantilie, Radu, A simple proof of the de Rham decomposition theorem, Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 36, No. 3-4, 341-343 (1992). ZBL0811.53040.
2
votes
Geodesics on the sphere
I don't know that these are correct or not.
The simplest way (in practice ) that come to my mind is the following trick. Consider two points $p$ and $q$ on sphere. connect them by an straight line …