Hyperbolic rigid motion

Printable View

• March 25th 2010, 11:51 AM
Pinkk
Hyperbolic rigid motion
Let $AB$ and $CD$ be geodesic segments of equal length. Prove that there is a hyperbolic rigid motion that maps $A$ and $AB$ onto $C$ and $CD$, respectively.

Once again, completely lost. (Headbang)
• March 29th 2010, 06:00 PM
Pinkk
Any suggestions?
• April 5th 2010, 03:48 PM
Pinkk
Okay, so I know the cases will probably have to divided up depending on if the geodesic segments are vertical lines or arcs of circles centered on the x-axis, and there has to be some inversion(s), but after that point I am just not sure.
• April 5th 2010, 06:21 PM
xxp9
so you're using the upper plane model of the hyperbolic geometry, are you?
• April 5th 2010, 06:24 PM
Pinkk
Yes, the upper half plane, so the hyperbolic rigid motions we have covered so far are inversions where the center is located on the x-axis, horizontal translations, and reflections across vertical lines.