An elliptic with the fixed geodesic a vertical line through the origin. Less dramatic visuals, but still interesting. This is the first of the set to simultaneously show a length preserving transform both of Euclidean space and of hyperbolic space in the upper half space model.pic.twitter.com/wOXUjLgRcH
Is there a transformation which turns the c one into a plane, while turning the plane it touces into a cone?
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Good question. There is not. The plane is the “plane-at-infinity”, and all hyperbolic isometries will keep its points ideal. Likewise, the finite points on the cone will always remain finite. Ideal points are not actually part of hyperbolic space. https://en.m.wikipedia.org/wiki/Ideal_point …
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