- #1
ivl
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Hi all!
I am reading a book on Classical Electrodynamics (Hehl and Obukhov, Foundations of Classical Electrodynamics, Birkhauser, 2003). In this manual I found the following statement:
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Consider a 4-dimensional differentiable manifold which is:
-connected (every 2 points are connected by continuous curve)
-Hausdorff (http://en.wikipedia.org/wiki/Hausdorff_space#Definitions)
-orientable (http://en.wikipedia.org/wiki/Orientability#Orientation_of_differential_manifolds)
-paracompact (manifold covered by finite number of coordinate charts)
This manifold always has a foliation by 3-dimensional hypersurfaces (each hypersurface is a hypersurface of constant "time").
============
Does anyone know another reference which confirms this statement? In other words, do you know why a connected Hausdorff orientable paracompact manifold always has such foliation?
Any help is massively appreciated!
Cheers!
I am reading a book on Classical Electrodynamics (Hehl and Obukhov, Foundations of Classical Electrodynamics, Birkhauser, 2003). In this manual I found the following statement:
============
Consider a 4-dimensional differentiable manifold which is:
-connected (every 2 points are connected by continuous curve)
-Hausdorff (http://en.wikipedia.org/wiki/Hausdorff_space#Definitions)
-orientable (http://en.wikipedia.org/wiki/Orientability#Orientation_of_differential_manifolds)
-paracompact (manifold covered by finite number of coordinate charts)
This manifold always has a foliation by 3-dimensional hypersurfaces (each hypersurface is a hypersurface of constant "time").
============
Does anyone know another reference which confirms this statement? In other words, do you know why a connected Hausdorff orientable paracompact manifold always has such foliation?
Any help is massively appreciated!
Cheers!