Hyperboloid model

The hyperboloid model of the curvature-minus-one hyperbolic plane is

{x \in R^{3} : - x_{0}^{2} + x_{1}^{2} + x_{2}^{2} = - 1, x_{0} > 0} .

(137)

Its metric is the restriction of the Minkowski bilinear form to tangent planes, and its geodesics are intersections with two-dimensional linear subspaces through the origin.

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- Minkowski inner product Hyperboloid model 13

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Hyperbolic geometry
Geometry and topology
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