In hyperbolic geometry 3d hemisphere is used for transformation between 2d disc models of Klein and Poincare. Can we use the 4d hemisphere for transformation between 3d Poincare and Klein models
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Your question is rather vaguely stated. Can you be more explicit either with concrete definitions or references? – Lee Mosher Jun 09 '20 at 16:07
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https://en.wikipedia.org/wiki/File:Relation5models.png – Alparslan Özafşar Jun 10 '20 at 00:15
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This shape explains transformation between 2D disc models. If we use 4D hemisphere, could we transform object between 3D hyperbolic Poincare and Beltrami ball models? – Alparslan Özafşar Jun 10 '20 at 00:20
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For example, streographicly project of the vertices of an 3d cube in Poincare model from 0,0,0,-1 to 4D sphere then delete w coordinates would give the beltrami coordinate of the cube? – Alparslan Özafşar Jun 10 '20 at 00:34
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Namely, would this picture work in one upper dimension? – Alparslan Özafşar Jun 10 '20 at 00:47