The natural bundles admitting natural lifting of linear connections

• Autorzy: Mikulski W.
• Języki publikacji: EN

Abstrakty

EN

Natural bundles admitting natural lifting of linear connections are characterized. Corollaries are presented. Some other similar results are obtained, too.

Słowa kluczowe

EN

classical linear connection; Riemannian tensor; natural bundle; natural operator

PL

klasyczne koneksje linearne; tensory Riemanniana; operatory naturalne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 1
• Strony: 223--232
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Mikulski W.

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

Bibliografia

• [1] S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, vol. 1, Intersciences, New York 1963.
• [2] I. Kolář, Torsion-free connections on higher order frame bundles, L. Tamássy and J. Szenthe (eds), New Developments in Differential Geometry, Kluver Academic Publishers (Netherland) 1996, 233-241.
• [3] I. Kolář at all, Natural Operations in Differential Geometry, Springer-Verlag, Berlin 1993.
• [4] M. Kureš, Natural lifts of classical linear connections to the cotangent bundle, Suppl. Rend. Circolo Mat. Palermo II 43 (1996), 181-187.
• [5] W. M. Mikulski, Non-existence of some canonical constructions on connections, Comment. Math. Univ. Carolinae 44.4 (2003), 691-695.
• [6] A. Morimoto, Prolongations of connections to bundles of infinitely near points, J. Diff. Geometry 11(1976), 476-498.
• [7] M. Paluszny, A. Zajtz, Foundation of the geometry of natural bundles, Lect. Notes Univ. Caracas, 1984.
• [8] K. Yano, E. M. Patterson, Vertical and complete lifts from a manifold to its cotangent bundle, J. Math. Soc. Japan 19(1967), 91-113.