Geodesic
The Double Exponential Map on Spaces of Constant Curvature
Matematičeskie trudy, Tome 10 (2007) no. 1, pp. 141-153.

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In the article, we derive an explicit formula for the double exponential map on spaces of constant curvature. In addition, we consider some applications of the resulting formula to computing the principal symbol of the product of two pseudodifferential operators on a manifold with connection. 
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V. V. Dzhepko; Yu. G. Nikonorov. The Double Exponential Map on Spaces of Constant Curvature. Matematičeskie trudy, Tome 10 (2007) no. 1, pp. 141-153. http://geodesic.mathdoc.fr/item/MT_2007_10_1_a5/

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