Bundle functors with the point property which admit prolongation of connections

W. M. Mikulski¹

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

Annales Polonici Mathematici, Tome 97 (2010) no. 3, pp. 253-256.

Résumé

Let $F:\mathcal M f\to\mathcal F\cal M$ be a bundle functor with the point property $F(pt)=pt$, where $pt$ is a one-point manifold. We prove that $F$ is product preserving if and only if for any $m$ and $n$ there is an $\cal F\cal M_{m,n}$-canonical construction $D$ of general connections $D({\mit\Gamma})$ on $Fp:FY\to FM$ from general connections $\mit\Gamma$ on fibred manifolds $p:Y\to M$.

Détail

DOI : 10.4064/ap97-3-4

Keywords: mathcal mathcal cal bundle functor point property where one point manifold prove product preserving only there cal cal canonical construction general connections mit gamma to general connections mit gamma fibred manifolds