
Re: gravity and topology
Posted:
Jun 30, 2012 11:21 PM


On Jun 30, 8:08 pm, Shmuel (Seymour J.) Metz <spamt...@library.lspace.org.invalid> wrote: > In <lSdnb2CT9QyznrS4p2d...@giganews.com>, on 06/24/2012 > at 12:51 PM, Tom Roberts <tjroberts...@sbcglobal.net> said: > > >I forgot to point out that for a manifold with metric (i.e. with > >geometry), the topology must be consistent with the curvature of > >the metric. For instance, the plane R^2 admits a flat metric > >(Euclidean geometry), or a metric with negative curvature > >(hyperbolic or Lobachevsky geometry), but does not admit a metric > >with positive curvature (which inherently requires periodicity). > > False. R^2 is diffeomorphic to a patch on a sphere. That > diffeomorphism gives you a metric on R^2 with positive curvature. > >  > Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel> > > Unsolicited bulk Email subject to legal action. I reserve the > right to publicly post or ridicule any abusive Email. Reply to > domain Patriot dot net user shmuel+news to contact me. Do not > reply to spamt...@library.lspace.org > >
Dimension is spherical for gravity and higher for the round 4th Dimension.

