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**Non-Riemannian Geommetry ??**

in Riemann Geommetry one needs a metric to define a distance so

[tex] ds^{2}= g_{i,j}dx^{i}dx^{j} [/tex] is a Bilinear form

the idea is can this be generalized to a non-metric Geommetry ? i mean, you define the distance via a function F so

[tex] ds^{2}= F(x_{i} , x_{j},dx_í} , dx_{j} ) [/tex]

so this time we do not have a Bilinear form or we do not have or depend on a metric [tex] g_{i,j} [/tex] is this the Non-Riemannian Geommetry ??