Usually when gravitational lensing is discussed, the examples are those of matter bending spacetime into a positive curvature. https://commons.wikimedia.org/wiki/File:Gravitational_lens-full.jpg In these cases, distortion of light is clearly evident as images of galaxies from behind these "gravitational lenses" are warped drastically. The below is one clear example of this distortion: https://commons.wikimedia.org/wiki/File:A_Horseshoe_Einstein_Ring_from_Hubble.JPG There appears to be far less mention of the idea of hyperbolic space curvature, which is has negative curvature in the Gaussian sense. To illustrate what this looks like, here is an depiction of a Hyperbolic 3-manifold: https://en.wikipedia.org/wiki/Hyper...erbolic_orthogonal_dodecahedral_honeycomb.png Based on what I have read on hyperbolic space, it doesn't seem to me that the Hyperbolic space would cause significant (obvious) distortions like we see in examples of gravitational lensing. If I understand correctly, hyperbolic space would not causes images of celestial objects to flip upside down, nor would they turn them into highly-distorted rings. However, it does seem that it would cause objects to appear farther than the really are. To get an appreciation of hyperbolic space, the folks from Numberphile posted a few videos on the subject of hyperbolic space: Playing Sports in Hyperbolic Space - Numberphile More Hyperbolic Sports - Numberphile Now for the big question: How significant could this hyperbolic curvature be without it being obvious that it exists? To take this idea to the limit, could we actually be in an universe where galaxies, or even stars, are orders of magnitude closer than we think, and that the only reason why it does not appear that way is optical trickery due to negatively curved space? Can Hyperbolic Space be affecting our view of the universe? Sincerely, Kevin M.