It is an intrinsically non-metrical geometry, whose facts are independent of any metric structure.

The result using the Euclidean metric structure is not optimal.

The example below shows the African 3:2 cross-rhythm within its proper metric structure.

A result of and shows that every metric structure on a surface arises from a local embedding in E.

This equation shows once more that parallel transport depends only on the metric structure so is an intrinsic invariant of the surface.

Kuratowski's research mainly focused on abstract topological and metric structures.

It is performed with an usul (metric structure).

In affine geometry, there is no metric structure but the parallel postulate does hold.

All of these songs share the same metric structure.

The subdivisions are grouped (beamed) in sets of four to reflect the proper metric structure.