The natural operators of general affine connections into general affine connections

Jan Kurek, Włodzimierz M. Mikulski

Abstract


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

Keywords


General affine connection; natural operator

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References


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.




DOI: http://dx.doi.org/10.17951/a.2017.71.1.61
Data publikacji: 2017-06-30 17:33:55
Data złożenia artykułu: 2017-06-30 12:58:04

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Copyright (c) 2017 Jan Kurek, Włodzimierz M. Mikulski