Pseudométrie

Pseudométrie, also known as pseudometry, is a branch of geometry that deals with the study of congruence and direct adsorption in spaces of higher dimensions. It originated from the theory of manifolds and topology, particularly from the works of mathematicians such as Charles Chevalley and Kentaro Yano.

In pseudométrie, relationships between geometric objects are studied under a condition of direct adjacency rather than a strict congruence. This means that certain properties of spaces, like the length of curves or the properties of angles, do not necessarily remain the same under a given transformation. This idea is opposed to the traditional notion of metric space, which relies on the preservation of distance and angles between points.

Pseudométrie is characterized by the introduction of new geometric objects, typically subject to transformation rules that allow for direct adjacency. These transformations can change the fundamental properties of the space in question. A key problem in pseudométrie is to determine the conditions under which these transformations are valid.

Applications of pseudométrie extend to various fields of mathematics and physics. In some areas of differential geometry and topology, pseudométrie is used as a tool to define and study so-called `pseudoriemannian manifolds' or Riemannian manifolds with additional structures.