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.
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1I don't know this subject, but the phrase "spherical spaces" might be worth searching with. For example, Leonard M. Blumenthal's 1935 paper Concerning spherical spaces seems somewhat relevant, at least the first page of it (this is all that I have access to). – Dave L. Renfro Jun 17 '14 at 20:24
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The correct term, for reasons I don't really understand, is elliptic geometry.
Qiaochu Yuan
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Because the sectional curvature is +1 as opposed to -1 in the case of hyperbolic geometry. – Moishe Kohan Jun 17 '14 at 20:44
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Although typically elliptic geometry refers more to geometry in $\Bbb RP^n$ than in $S^n$. – Ted Shifrin Jun 17 '14 at 20:45
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@studiosus: right, and "hyperbolic geometry" also allows the geometry of hyperbolic manifolds not homeomorphic to $\mathbb{H}^n$. I'm not really asking for an answer to this question, just trying to communicate the source of my confusion. – Qiaochu Yuan Jun 17 '14 at 21:08
