Publications de l'Institut Mathématique, Nouvelle Série Vol. 97(111), pp. 149–160 (2015) 

THE INDUCED CONNECTIONS ON TOTAL SPACES OF FIBRED MANIFOLDSWlodzimierz M. MikulskiInstitute of Mathematics, Jagiellonian University, Cracow, PolandAbstract: Let $Y\to M$ be a fibred manifold with $m$dimensional base and $n$dimensional fibres. If $m\geq 2$ and $n\geq 3$, we classify all linear connections $A(\Gamma,\Lambda,\Theta):TY\to J^1(TY\to Y)$ in $TY\to Y$ (i.e., classical linear connections on $Y$) depending canonically on a system $(\Gamma,\Lambda,\Theta)$ consisting of a general connection $\Gamma:Y\to J^1Y$ in $Y\to M$, a torsion free classical linear connection $\Lambda:TM\to J^1(TM\to M)$ on $M$ and a linear connection $\Theta:VY\to J^1(VY\to Y)$ in the vertical bundle $VY\to Y$. Keywords: general connection; linear connection; natural operator Classification (MSC2000): 53C05; 58A32 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 16 Apr 2015. This page was last modified: 21 Apr 2015.
© 2015 Mathematical Institute of the Serbian Academy of Science and Arts
