n-spherical geometry

Question

I'm interested in spherical geometry on the n-sphere. Surely this has been done, but I can't find anything online. Where? No luck with n-spherical geometry, hyperspherical geometry, or higher dimensional spherical geometry.

Answer 1

The correct term, for reasons I don't really understand, is elliptic geometry.

Answer 2

Try Volume 2 of M.Berger, "Geometry", chapters 18, 19.