Horizontal extension of connections into (2)-connections

• Autorzy: Doupovec M. , Mikulski W. M.
• Języki publikacji: EN

Abstrakty

EN

We discuss the prolongation of connections to to some non product preserving bundles. We introduce the concept of (r)-connection on a fibered manifold Y and for a given connection F on Y we construct its horizontal extension F(2). We also prove that F(2 ) is the unique (2)-connection on Y canonically dependent on F.

Słowa kluczowe

EN

natural operator; horizontal extension; connection; differential geometry

PL

operatory naturalne; rozszerzenia poziome; koneksja

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2004
• Tom: Vol. 37, nr 4
• Strony: 963--975
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Doupovec M.

• Department of Mathematics, Brno University of Technology, FSI VUT Brno, Technická 2, 616 69 Brno, Czech Republic

autor

Mikulski W. M.

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Bibliografia

• [1] I. Kolář, On generalized connections, Beiträge zur Algebra und Geometrie 11 (1981), 29-34.
• [2] I. Kolář, P. W. Michor, J. Slovák, Natural Operations in Differential Geometry, Springer, Berlin, 1993.
• [3] J. Slovák, Prolongations of connections and sprays with respect to Weil functors, Suppl. Rend. Circ. Mat. Palermo, Serie II 14 (1987), 143-155.