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Two-dimensional hyperbolic metric in polar coordinates ( $d s^{2} = a^{2} (d r^{2} + sinh^{2} r d ϕ^{2})$ )

This metric is the hyperbolic plane with curvature scale

a

. Its nonzero connection coefficients are

Γ_{ϕϕ}^{r} = - sinh r cosh r, Γ_{r ϕ}^{ϕ} = Γ_{ϕ r}^{ϕ} = coth r .

Table of contents 64 2
- Coordinate geodesics of the hyperbolic polar metric Two-dimensional hyperbolic metric in polar coordinates 16
- Curvature of the two-dimensional hyperbolic polar metric Two-dimensional hyperbolic metric in polar coordinates 27

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