Negative answers to some questions about constructions on connections

• Autorzy: Mikulski W.
• Języki publikacji: EN

Abstrakty

EN

Let m and n be natural numbers. For an arbitrary bundle functor G on the category FMm,n of fibred manifolds with m-dimensional bases and n-dimensional fibers and their local fibered diffeomorphisms we prove that there is no FMm,n-natural operator V transforming general connections.

Słowa kluczowe

EN

general connection; classical connection; linear connection; bundle functor; natural operators

PL

związek klasyczny; związek linearny; związek ogólny; funktory; operatory naturalne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 3
• Strony: 685--689
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Mikulski W.

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

Bibliografia

• [1] J. Gancarzewicz, I. Kolář, Some gauge-natural operators on linear connections, Mh. Math. 111 (1991), 23-33.
• [2] I. Kolář, Some gauge-natural operators on connections, Colloq. Math. Soc. J. Bolyai 56. Differential Geometry, Eger (Hungary), 1989, 435-445.
• [3] I. Kolář, Prolongations of generalized connections, Colloq. Math. Soc. J. Bolyai 31. Differential Geometry, Budapest (Hungary), 1979, 317-325.
• [4] I. Kolář, P. W. Michor, J. Slovák, Natural Operations in Differential Geometry, Springer-Verlag, 1993.
• [5] W. M. Mikulski, Non-existence of some canonical constructions on connections, Comment. Math. Univ. Carolinae 44.4 (2003), 691-695.