On “special” fibred coordinates for general and classical connections

Włodzimierz M. Mikulski¹

¹ Institute of Mathematics Jagiellonian University Łojasiewicza 6 30-348 Kraków, Poland

Annales Polonici Mathematici, Tome 99 (2010) no. 1, pp. 99-105.

Résumé

Using a general connection $\mit\Gamma$ on a fibred manifold $p:Y\to M$ and a torsion free classical linear connection $\nabla$ on $M$, we distinguish some “special” fibred coordinate systems on $Y$, and then we construct a general connection $ \widetilde{\mathcal{F}}({\mit\Gamma},\nabla)$ on $Fp:FY\rightarrow FM$ for any vector bundle functor $F: \mathcal{M}f\rightarrow\mathcal{V}\mathcal{B}$ of finite order.

Détail

DOI : 10.4064/ap99-1-9

Keywords: using general connection mit gamma fibred manifold torsion classical linear connection nabla distinguish special fibred coordinate systems construct general connection widetilde mathcal mit gamma nabla rightarrow vector bundle functor mathcal rightarrow mathcal mathcal finite order