# Non-Riemannian Geommetry ?

## Main Question or Discussion Point

Non-Riemannian Geommetry ??

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

$$ds^{2}= g_{i,j}dx^{i}dx^{j}$$ 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

$$ds^{2}= F(x_{i} , x_{j},dx_í} , dx_{j} )$$

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

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quasar987
Homework Helper
Gold Member
Re: Non-Riemannian Geommetry ??

The only example I know is Finsler geometry.

Ben Niehoff