At a first glance, this part of my exploration has nothing to do with the deformed tensor products. It started a long time ago (around 1974-1976) with the help of a small leaflet introducing the basic stones for tensor calculus (*extern link Wikipedia-GB). The end of that leaflet contained one chapter describing how it was possible to build the first necessary ingredient needed by the general theory of relativity (GTR); namely: the Riemann’s curvature tensor*.

 

The author (A. Delachet) insisted on the first order variations of the basis vectors. And this insistence has been my initial motivation for a pure intellectual curiosity asking: “What happens when the second, third, … order variations of the basis vectors are incorporated into the calculations?”

 

© Thierry PERIAT, 09 January 2019.

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