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Keywords:
general connection; linear connection; natural operator
general connection; linear connection; natural operator
Summary:
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.
References:
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