I am currently trying to connect Hyperbolic geometry through several models with Riemannian geometry. At first I have transformed the metric tensor from sphere in $R^3$ and the pseudo-sphere in $R^{2,1}$ through stereographic projection, complex transformations etc. After that I am trying to transform the induced symmetries(independent Killing vectors) of $R^3$ and $R^{2,1}$ on the sphere and pseudo-sphere in all these several coordinate system. This process is supposed to reveal the Riemannian structure of hyperbolic spaces. I need some help to make the connection. Thank you
2026-03-26 22:13:51.1774563231
Riemannian geometry and Symmetries, Hyperbolic Spaces
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