Timeline for Hyperbolicity on Riemann Surfaces
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Aug 21, 2011 at 10:45 | history | edited | R W | CC BY-SA 3.0 |
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| Aug 19, 2011 at 15:47 | comment | added | ght | Given a Riemann surface you can always put a metric on it and consider it as a metric space. Therefore, both notions of hyperbolicity make sense. A connected metric surface is a quotient of one of the following - the sphere (curvature +1) - the Euclidean plane (curvature 0) - the hyperbolic plane (curvature −1). by a free action of a discrete subgroup of isometries. Hence, with this notion the torus is a Riemann surface and manifold who is of parabolic type. Other thing is that ALL compact metric spaces are indeed Gromov hyperbolic so the torus is Gromov hyperbolic. | |
| Aug 19, 2011 at 14:50 | comment | added | Autumn Kent | Seeing that compact metric spaces are Gromov hyperbolic, I think it's perfectly fair to call them Gromov hyperbolic. | |
| Aug 19, 2011 at 14:08 | history | answered | R W | CC BY-SA 3.0 |