Seminar : Boris KOLEV

From Hooke's law to Einstein's equation: objective derivatives as covariant derivatives on the variety of Riemannian metrics

Abstract

The subject of objective derivatives in continuum mechanics has a long and controversial history. Several works deal with the formulation of the correct mathematical definition of what they really are and try to unify them all in a single definition (or a single family). In a recent work, in collaboration with Rodrigue Desmorat, we show, finally, that they all correspond in fact to covariant derivatives on the infinite dimensional variety of all Riemannian metrics on the Body. Moreover, a rule of Leibniz, which allows to pass from an objective derivative on contravariant tensors to a derivative on covariant tensors, and vice versa, makes their classification between those of "Lie derivative" type and those of "co-rotational" type artificial.

Lien de connexion : Zoom, ID de réunion : 876 2383 9103