Geodesic
The canonical constructions of connections on total spaces of fibred manifolds
Archivum mathematicum, Tome 60 (2024) no. 3, pp. 163-175 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.5817/AM2024-3-163
Classification : 53C05, 58A32
Keywords: general connection; linear connection; natural operator 
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Mikulski, Włodzimierz M. The canonical constructions of connections on total spaces of fibred manifolds. Archivum mathematicum, Tome 60 (2024) no. 3, pp. 163-175. doi: 10.5817/AM2024-3-163

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