On the geometry of vertical Weil bundles

Ivan Kolář

Address: Institute of Mathematics and Statistics, Masaryk University, Kotlářská 2, CZ 611 37 Brno, Czech Republic

E-mail: kolar@math.muni.cz

Abstract: We describe some general geometric properties of the fiber product preserving bundle functors. Special attention is paid to the vertical Weil bundles. We discuss namely the flow natural maps and the functorial prolongation of connections.

AMSclassification: primary 58A20; secondary 58A32, 53C05.

Keywords: Weil bundle, fiber product preserving bundle functor, flow natural map, weak principal connection.

DOI: 10.5817/AM2014-5-317