Curvature tensor and deformed tensor products

Go to the "Table of contents".

Document: see it on the french version of this page (follow the link).

Comments:

The theory studying deformed tensor products is able to propose a procedure furnishing the components of a pseudo curvature tensor.

The document:

- exposes the procedure;

- compares the properties of the components of the pseudo curvature tensor with those of the Riemann's curvature tensor;

- states that these components coincide when the second partial derivatives of the components of the (supposed symmetric) metric vanish;

- rediscover the hight connexion between these mathematical considerations and the important concept of aera metrics initiated in 1933 by E. Cartan;

- gives now a precise meaning to any non-trivial decomposition in the theory of the (E) question (see the chapter proposing methods to get them).

This document is a milestone in my progression because it makes a junction with the well-accepted works of celebrated old masters: Riemann, Christoffel and Cartan.

The next step will have to discover the situations which are uncovered by these works but may eventually have some importance for physics.

Go back to the page: "Mathematical tools". 

Last edited: 15/09/2021