Address: Institute of Mathematics, Jagiellonian University, Cracow, Poland
E-mail: Wlodzimierz.Mikulski@im.uj.edu.pl
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.
AMSclassification: primary 53C05; secondary 58A32.
Keywords: general connection, linear connection, natural operator.
DOI: 10.5817/AM2024-3-163