Geodesic
On the Kolář connection
Archivum mathematicum, Tome 49 (2013) no. 4, pp. 223-240 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $Y\rightarrow M$ be a fibred manifold with $m$-dimensional base and $n$-dimensional fibres and $E\rightarrow M$ be a vector bundle with the same base $M$ and with $n$-dimensional fibres (the same $n$). If $m\ge 2$ and $n\ge 3$, we classify all canonical constructions of a classical linear connection $A(\Gamma ,\Lambda ,\Phi ,\Delta )$ on $Y$ from a system $(\Gamma ,\Lambda ,\Phi ,\Delta )$ consisting of a general connection $\Gamma $ on $Y\rightarrow M$, a torsion free classical linear connection $\Lambda $ on $M$, a vertical parallelism $\Phi \colon Y\times _ME\rightarrow VY$ on $Y$ and a linear connection $\Delta $ on $E\rightarrow M$. An example of such $A(\Gamma ,\Lambda ,\Phi ,\Delta )$ is the connection $(\Gamma ,\Lambda ,\Phi ,\Delta )$ by I. Kolář.
Let $Y\rightarrow M$ be a fibred manifold with $m$-dimensional base and $n$-dimensional fibres and $E\rightarrow M$ be a vector bundle with the same base $M$ and with $n$-dimensional fibres (the same $n$). If $m\ge 2$ and $n\ge 3$, we classify all canonical constructions of a classical linear connection $A(\Gamma ,\Lambda ,\Phi ,\Delta )$ on $Y$ from a system $(\Gamma ,\Lambda ,\Phi ,\Delta )$ consisting of a general connection $\Gamma $ on $Y\rightarrow M$, a torsion free classical linear connection $\Lambda $ on $M$, a vertical parallelism $\Phi \colon Y\times _ME\rightarrow VY$ on $Y$ and a linear connection $\Delta $ on $E\rightarrow M$. An example of such $A(\Gamma ,\Lambda ,\Phi ,\Delta )$ is the connection $(\Gamma ,\Lambda ,\Phi ,\Delta )$ by I. Kolář.
DOI : 10.5817/AM2013-4-223
Classification : 53C05, 58A32
Keywords: general connection; linear connection; classical linear connection; vertical parallelism; natural operators 
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     author = {Mikulski, W{\l}odzimierz M.},
     title = {On the {Kol\'a\v{r}} connection},
     journal = {Archivum mathematicum},
     pages = {223--240},
     year = {2013},
     volume = {49},
     number = {4},
     doi = {10.5817/AM2013-4-223},
     mrnumber = {3159312},
     zbl = {1299.53071},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2013-4-223/}
}
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Mikulski, Włodzimierz M. On the Kolář connection. Archivum mathematicum, Tome 49 (2013) no. 4, pp. 223-240. doi: 10.5817/AM2013-4-223

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