On the existence of prolongations of connections by bundle functors
- Autores: Wlodzimierz M. Mikulski
- Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 22, Nº 3, 2007, págs. 297-314
- Idioma: inglés
- Enlaces
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Resumen
We construct canonically a general connection AF (¡;r) on Fp : FY ! FM from a general connection ¡ on a ¯bred manifold p : Y ! M by means of a projectable classical linear connection r on Y , where F : Mf ! VB is a vector bundle functor. In the case of a not necessarily vector bundle functor F : Mf ! FM we ¯nd some simple equivalent condition on the existence of a general connection A(¡;r) on Fp : FY ! FM from a general connection ¡ on Y ! M by means of a projectable classical linear connection r on Y . We present a construction of a classical linear connection AF (r) on FY from a projectable classical linear connection r on Y for any ¯ber product preserving bundle functor F : FMm ! FM. We characterize bundle functors F : FMm;n ! FM which admit a construction of a classical linear connection A(r) on FY from a projectable classical linear connection r on Y . We characterize gauge bundle functors F : VBm;n ! FM which admit a construction of a classical linear connection A(D;r) on FE from a linear general connection D on E ! M by means of a classical linear connection r on M.
