JP Journal of Geometry and Topology
Volume 7, Issue 1, Pages 65 - 113
(March 2007)
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GEOMETRICAL THEORY ON COMBINATORIAL MANIFOLDS
Linfan Mao (P. R. China)
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Abstract:
For an integer 
a combinatorial manifold  is defined to be a
geometrical object  such that for 
there is a local chart 
enable  with 
 where 
is an  -ball for
integers  Topological
and differential structures such as those
of d-pathwise connected, homotopy classes, fundamental d-groups in
topology and tangent vector fields, tensor fields, connections, Minkowski
norms in differential geometry on these finitely combinatorial manifolds are
introduced. Some classical results are generalized to finitely combinatorial
manifolds. Euler-Poincaré characteristic is discussed and geometrical
inclusions in Smarandache geometries for various geometries are also presented
by the geometrical theory on finitely combinatorial manifolds in this paper. |
| Keywords and phrases: manifold, finitely combinatorial manifold, topological structure, differential structure, combinatorially Riemannian geometry, combinatorially Finsler geometry, Euler-Poincaré characteristic. |
| Communicated by Yasuo Matsushita |
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