I copy some comments about orbifolds that look to be a generalization
of manifolds, comments from Dr. Howard Iseri, I hope he agrees.

--- Howard Iseri <hiseri@...> wrote:
> Basically what I know is this. A Riemannian manifold
> is a manifold that has
> the same local geometry as an elliptic, Euclidean,
> or hyperbolic geometry
> (in some particular dimension).

does it mean that a riemann manifold should have at least one of them
(either elliptic, or euclidean, or hiperbolic geometry)?

>An orbifold
> generalizes this by allowing
> local geometries that are like one of these mod some
> symmetry group.

i don't understand it well: how is a say local elliptic geometry
modulo a symmetry group?

i guess, i feel the smarandache geometries can be put in orbifolds
somehow...

> For
> example, the plane mod the group generated by a 180
> degree rotation is a
> cone (cut the plane and wrap it around twice so that
> a point is identified
> with its image from a 180 degree rotation). An
> orbifold can have a point
> where the local geometry is the same as the geometry
> around the vertex of
> the cone. The manifolds in my book are similar to
> this, but the possible
> cones are different.
>
> Howard.
>
> At 02:44 PM 2/5/03 -0800, you wrote:
> >still no clear definition...
> >
> >--- Howard Iseri <hiseri@...> wrote:
> > > Hi Minh,
> > >
> > > The Geometry Center has some stuff. You should
> be
> > > able to get there from
> > > this site.
> > >
> > > http://www.geom.umn.edu/apps/pinball/about.html
> > >
> > > Howard.
> > >
> > >
> > > At 01:20 PM 2/5/03 -0800, you wrote:
> > > >What is the scientific definition of an
> ORBIFOLD?
> > > >Any site explaining?
> > > >
> > > >=====
> > > >Sincerely,
> > > >
> > > >Dr. M. L. Perez
> > > >American Research Press
> > > >Rehoboth, Box 141, NM 87322, USA
> > > >E-Mail: M_L_Perez@...
> > > >http://www.gallup.unm.edu/~smarandache/
> > > >
> > >