Champs de tenseurs. Bases mobiles et naturelles. Torsion. Courbure

Marc Renaud 1
1 LAAS-RAP - Équipe Robotique, Action et Perception
LAAS - Laboratoire d'analyse et d'architecture des systèmes [Toulouse]
Abstract : The aim of this research report is to study the fields independent of any differential geometry connection and then those that depend on it. In this second case, the emphasis is mainly put on the calculation of the torsion and curvature tensor fields of the connection depending on whether the variety is arbitrary or Riemannian (i.e., with a very special tensor field called metric). When the variety is Riemannian the calculations are made for any connection and for a connection adapted to the so-called Riemannian connection metric. The objective is to specify much better than the various references indicated in the bibliography in which precise framework the calculations are made (connection or not? any variety or a Riemannian one? any connection or a Riemannian one?).
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Technical Reports
Rapport LAAS n° 17123. 2017, 199p
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Marc Renaud. Champs de tenseurs. Bases mobiles et naturelles. Torsion. Courbure. Rapport LAAS n° 17123. 2017, 199p. 〈hal-01523409〉

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