# Sci-fi story with the premise that spacetime geometry is Riemannian

I'm trying to find a hard sci-fi story where one of the major premises was that the world has a Riemannian geometry (x^2+y^2+z^2 + t^2) instead of the real world's Minkowski geometry (x^2+y^2+z^2 - t^2). The effects of this on relativity and how it affected the world were very significant. Here's some of the effects that I remember:

• Stars, instead of looking like points of white light, looked like lines that were cross-sections of a rainbow
• It was impossible for two objects to collide with certain velocities unless a third object was also present
• It was possible to "turn around" your direction through time, just as it's possible to turn around the direction you're moving through space in the real world

I remember seeing this online several years ago, along with an out-of-character analysis of the setting that explained all of the above effects in detail. Does anyone know what this is and/or where I found it?

• Welcome to Science Fiction & Fantasy! This question would be improved by going through the checklists here; How to ask a good story-ID question? – Stormblessed Nov 29 '18 at 4:49
• @Loki it's indeed called Riemannian, not Euclidean. – Joseph Sible-Reinstate Monica Nov 29 '18 at 23:28
• @JosephSible Riemannian manifolds is the more general term, it contains both Minkowski and Euclidean metrics. Feel free to check Wikipedia. – Hans Olo Nov 30 '18 at 7:29
• @Loki I meant that now that it's been answered, I've confirmed that Riemannian is the major term the author uses to describe it, so even if Euclidean would be more correct from a technical perspective, Riemannian is much more helpful for anyone else who would search for this question. – Joseph Sible-Reinstate Monica Nov 30 '18 at 13:16
• @Rebel-Scum: Minkowski is pseuso-Riemannian. Riemannian it is not. – Incnis Mrsi May 18 '20 at 16:05