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[3] viXra:2402.0143 [pdf] submitted on 2024-02-24 21:30:27
Authors: Abdelmajid Ben Hadj Salem
Comments: 63 Pages. In French
In this fascicle, we give some complementary elements concerning the theory of surfaces like the lines of curvature, the asymptotic lines.
Category: Geometry
[2] viXra:2402.0116 [pdf] submitted on 2024-02-21 20:39:23
Authors: Ángel Blanco Nápoles
Comments: Spanish, Russian and English versions. 14 pages each. 14 drawings.
This work reveals the antagonistic and unsolvable internal contradictions of the Euclidean "geometry" of Philosophical Idealism with itself and with the mathematics that derives from it, also providing the definitive solution of Dialectical Materialism, which not only solves the aforementioned contradictions, but many others in the field of mathematics, physics, astronomy and cosmology.
Category: Geometry
[1] viXra:2402.0065 [pdf] replaced on 2024-07-10 23:30:25
Authors: Bin Wang
Comments: 20 Pages.
Let $X$ be a differential manifold. Let $mathscr D'(X)$ be the space of currents, and $S^{infty}(X)$ the Abelian group freely generated by regular cells, each of which is a pair of a polyhedron $Uppi$ and a ifferential embedding of a neighborhood of ${Uppi}$ to $X$. In this paper, we define a variant that is a bilinear map begin{equation}begin{array}{ccc} S^{infty}(X)times S^{infty}(X) &ightarrow & mathscr D'(X)(c_1, c_2) &ightarrow & [c_1wedge c_2]end{array}end{equation} called the supportive intersection such thatpar 1) the support of $[c_1wedge c_2]$ is contained in the intersection of the supports of $c_1, c_2$; 2) if $c_1, c_2$ are closed, $[c_1wedge c_2]$ is also closed and its cohomology class is the cup-product of the cohomology classes of $c_1, c_2$.
Category: Geometry
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