The natural operators of general affine connections into general affine connections

Jan Kurek; Włodzimierz M. Mikulski

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 71 (2017), / Harvested from The Polish Digital Mathematics Library

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Résumé

We reduce the problem of describing all $ℳ f_{m}$ -natural operators transforming general affine connections on $m$ -manifolds into general affine ones to the known description of all $G L (𝐑^{m})$ -invariant maps $𝐑^{m *} \otimes 𝐑^{m} \to \otimes^{k} 𝐑^{m *} \otimes \otimes^{k} 𝐑^{m}$ for $k = 1, 3$ .

Publié le : 2017-01-01
EUDML-ID : urn:eudml:doc:289733

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     author = {Jan Kurek and W\l odzimierz M. Mikulski},
     title = {The natural operators of general affine connections into general affine connections},
     journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
     volume = {71},
     year = {2017},
     language = {en},
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Jan Kurek; Włodzimierz M. Mikulski. The natural operators of general affine connections into general affine connections. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 71 (2017) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2017_71_1_61/

Bibliographie

Debecki, J., The natural operators transforming affinors to tensor fields of type (3, 3), Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 39 (2000), 37-49.

Kobayashi, S., Nomizu, K., Foundations of Differential Geometry. Vol. I, J. Wiley-Interscience, New York–London, 1963.

Kolar, I., Michor, P. W., Slovak, J., Natural Operations in Differential Geometry,

Springer-Verlag, Berlin, 1993.