Geodesic
Geometry on the Unit Ball of a Complex Hilbert Space
Canadian journal of mathematics, Tome 30 (1978) no. 1, pp. 22-31

Voir la notice de l'article provenant de la source Cambridge University Press

Furnishing the open unit ball of a complex Hilbert space with the Carathéodory-differential metric, we construct a model which plays a similar role as that of the Poincaré model for the hyperbolic geometry.In this note we study the question whether or not through a point in the model not lying on a given line there exists a unique perpendicular, and give a necessary and sufficient condition for the existence of a unique perpendicular. This enables us to divide a triangle into two right triangles. Many trigonometric identities in a general triangle are easy consequences of various identities which hold on a right triangle. 
Hahn, Kyong T. Geometry on the Unit Ball of a Complex Hilbert Space. Canadian journal of mathematics, Tome 30 (1978) no. 1, pp. 22-31. doi: 10.4153/CJM-1978-002-6
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