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A problem of integral geometry for tensor fields and the Saint Venant equation. (English. Russian original) Zbl 0538.53067
Sib. Math. J. 24, 968-977 (1983); translation from Sib. Mat. Zh. 24, No. 6(142), 176-187 (1983).
L’auteur montre qu’un champ fini de tenseurs symétriques de valence m sur \(R^ n\) est déterminé par ses intégrales sur tous les droites, de la m-forme générée par lui, jusqu’à un champ de tenseurs f de la forme \(f=\sigma \nabla x\) où x est un champ fini arbitraire de tenseurs symétriques de valence m-1, \(\nabla\) l’opérateur de différentiation et \(\sigma\) celui de symétrisation. On démontre ensuite, que l’équation \(\sigma \nabla x=f\) a une solution si et seulement si \(Vf=0\), où V est un certain opérateur sur l’espace des champs de tenseurs symétriques.
Reviewer: V.Cruceanu

MSC:
53C65 Integral geometry
53A45 Differential geometric aspects in vector and tensor analysis
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