Re: hyperbolic manifold

From: sylvain (sgolenia_at_freesurf.fr)
Date: 02/18/05 

Date: Fri, 18 Feb 2005 17:45:06 +0000 (UTC)

tessel@tum.bot wrote:
> On Fri, 4 Feb 2005, sylvain wrote:
>
> > Hi,
> > I study hamiltonians on configuration spaces of negative curvature
-1
> > which the mathematicians call hyperbolic. Does anyone know if these
> > spaces have physical meanings?
>
> Oh, my gosh, yes. In fact, Poincare developed the geometry of H^2
> partly with applications to classical dynamics in mind.
I see. Unfortunatly, I am more interested in the quantum mechanical
properties of operators (nature of the "continuous spectrum",
scattering...). This area has been really overdone in mathematics but I
am not convince that it is really physical. Any clue?

Question: Do we have any idea about the curvature of our universe ?

> A random recent
> example of interest in gravitation physics: a huge open question in
gtr
> concerns the nature of the geometry near "generic" curvature
> singularities in say vacuum solutions of the EFE.

could you translate me EFE ?

>(if
> you follow this up, eventually you'll find out what hyperbolic
geometry
> has to do with dynamical systems and the Riemann zeta function!).
Just a remark, I've seen once some guys trying to prove the Riemman
conjecture calculating the point spectrum of the laplacian on some
hyperbolic manifold.

Thanks your comments and help
Sylvain Golenia