The canonical constructions of connections on total spaces of fibred manifolds

Mikulski, Włodzimierz M.. "The canonical constructions of connections on total spaces of fibred manifolds." Archivum Mathematicum 060.3 (2024): 163-175. <http://eudml.org/doc/299553>.

@article{Mikulski2024,
abstract = {We classify classical linear connections $A(\Gamma ,\Lambda ,\Theta )$ on the total space $Y$ of a fibred manifold $Y\rightarrow M$ induced in a natural way by the following three objects: a general connection $\Gamma $ in $Y\rightarrow M$, a classical linear connection $\Lambda $ on $M$ and a linear connection $\Theta $ in the vertical bundle $VY\rightarrow Y$. The main result says that if $ \mathrm \{dim\}(M)\ge 3$ and $ \mathrm \{dim\}(Y)-\mathrm \{dim\}(M) \ge 3$ then the natural operators $A$ under consideration form the $17$ dimensional affine space.},
author = {Mikulski, Włodzimierz M.},
journal = {Archivum Mathematicum},
keywords = {general connection; linear connection; natural operator},
language = {eng},
number = {3},
pages = {163-175},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {The canonical constructions of connections on total spaces of fibred manifolds},
url = {http://eudml.org/doc/299553},
volume = {060},
year = {2024},
}

TY - JOUR
AU - Mikulski, Włodzimierz M.
TI - The canonical constructions of connections on total spaces of fibred manifolds
JO - Archivum Mathematicum
PY - 2024
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 060
IS - 3
SP - 163
EP - 175
AB - We classify classical linear connections $A(\Gamma ,\Lambda ,\Theta )$ on the total space $Y$ of a fibred manifold $Y\rightarrow M$ induced in a natural way by the following three objects: a general connection $\Gamma $ in $Y\rightarrow M$, a classical linear connection $\Lambda $ on $M$ and a linear connection $\Theta $ in the vertical bundle $VY\rightarrow Y$. The main result says that if $ \mathrm {dim}(M)\ge 3$ and $ \mathrm {dim}(Y)-\mathrm {dim}(M) \ge 3$ then the natural operators $A$ under consideration form the $17$ dimensional affine space.
LA - eng
KW - general connection; linear connection; natural operator
UR - http://eudml.org/doc/299553
ER -