## Geometrical Theory on Combinatorial Manifolds

**Authors:** Linfan Mao

For an integer m ≥ 1, a combinatorial manifold fM is defined to be
a geometrical object fM such that for (...), there is a local chart
(see paper)
where Bnij is an nij -ball for integers 1 ≤ j ≤ s(p) ≤ m. 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-Poincare 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.

**Comments:** 37 pages

**Download:** **PDF**

### Submission history

[v1] 19 Apr 2011

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