The natural operators of general affine connections into general affine connections
Jan Kurek; Włodzimierz M. Mikulski
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2017)
- Volume: 71, Issue: 1
- ISSN: 0365-1029
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topJan Kurek, and Włodzimierz M. Mikulski. "The natural operators of general affine connections into general affine connections." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 71.1 (2017): null. <http://eudml.org/doc/289733>.
@article{JanKurek2017,
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 $\mathbf \{R\}^\{m*\}\otimes \mathbf \{R\}^m\rightarrow \otimes ^k\mathbf \{R\}^\{m*\}\otimes \otimes ^k\mathbf \{R\}^m$ for $k=1,3$.},
author = {Jan Kurek, Włodzimierz M. Mikulski},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {General affine connection; natural operator},
language = {eng},
number = {1},
pages = {null},
title = {The natural operators of general affine connections into general affine connections},
url = {http://eudml.org/doc/289733},
volume = {71},
year = {2017},
}
TY - JOUR
AU - Jan Kurek
AU - Włodzimierz M. Mikulski
TI - The natural operators of general affine connections into general affine connections
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2017
VL - 71
IS - 1
SP - null
AB - 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 $\mathbf {R}^{m*}\otimes \mathbf {R}^m\rightarrow \otimes ^k\mathbf {R}^{m*}\otimes \otimes ^k\mathbf {R}^m$ for $k=1,3$.
LA - eng
KW - General affine connection; natural operator
UR - http://eudml.org/doc/289733
ER -
References
top- 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.
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