The natural linear operators Λp T* → TTr*

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

Abstrakty

EN

For integers p ≥ 0, n ≥ p+2 and r ≥ 1 all natural linear operators Λ^p T^*_|Mfn → TT^r* transforming p-forms from n-manifolds M into vector fields on the r-th order cotangent bundle T^r* M = J^r (M, R)₀ of M are completely described.

Słowa kluczowe

EN

natural bundle; natural operator

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2004
• Tom: Vol. 44, nr 1
• Strony: 127--136
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Mikulski W. M.

• Institute of Mathematics, Jagiellonian University, Kraków, Reymonta 4, Poland

Bibliografia

• [1] M. Doupovec and J. Kurek, Liftings of tensor fields to the cotangent bundles, Proc. Conf. Differential Geom. and Appl., Brno, 1995, 141-150.
• [2] M. Doupovec and J. Kurek, Some geometrical constructions with (0, 2)-tensor fields on higher order cotangent bundles, Ann. UMCS 50 (1996), 43-50.
• [3] M. Doupovec and J. Kurek, Torsions of connections on higher order cotangent bundles, Czechoslovak Math. J., to appear.
• [4] I. Kolár, P. W. Michor and J. Slovak, Natural Operations in Differential Geometry, Springer Verlag, Berlin, 1993.
• [5] J. Kurek, Natural affinors on higher order cotangent bundle functor, Arch. Math. Brno 28 (1992), 175-180.
• [6] J. Kurek, Natural transformations of higher order cotangent bundle functors, Ann. Polon. Math. 58 (1993), 29-35.
• [7] M. Kureš, Connections and torsions on TT*M, Annales UMCS 55 (2001), 89-101.
• [8] W. M. Mikulski, Some natural constructions on vector fields and higher order cotangent bundles, Mh. Math. 117 (1994), 107-119.
• [9] W. M. Mikulski, Natural functions on T*T(r) and T*Tr*, Arch. Math. Brno 31 (1995), 1-7.
• [10] W. M. Mikulski, Liftings of 1-forms to the linear r-tangent bundle, Arch. Math. Brno 31 (1995), 97-111.
• [11] K. Yano and S. Ishihara, Tangent and Cotangent Bundles, Marcel Dekker, INC., New York, 1973.