Bundles of contact elements on fibered fibered manifolds and the flow operator

• Autorzy: Mikulski W. , Tomas J.
• Języki publikacji: EN

Abstrakty

EN

We define the concept of a fibered fibered (k1, k2, l1, l2)- contact element of order (r1, . . . , r8) for r8 > r4 < r5 > r3, r8 > r6 < r7 > r2 and r1 < ri for ri = 2, 3, . . . , 8. For k1 < m1, k2 < m2, l1 < n1, l2 < n2, we define a bundle func tor Kr1,...,r8/ k1,k2,l1,l2 defined on the category FM2 m1,m2,n1,n2 of (m1,m2, n1,n2)-fibere fibered manifolds. We prove that the only natural transformation on the bundle functor Kr1,...r8/ k1,k2,l1,l2 is the identity one. Moreover, we prove that any natural operator lifting projectable vector fields Y to Kr1,...r8/ k1,k2,l1,l2 Y is a constant multiple of the flow operator.

Słowa kluczowe

EN

contact element; fibered manifold; bundle functors; natural operators; differential geometry

PL

elementy styczności; rozmaitość włóknista; wiązka punktorów; operatory naturalne; geometria różniczkowa

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2007
• Tom: Vol. 40, nr 2
• Strony: 485--493
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Mikulski W.

autor

Tomas J.

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

Bibliografia

• [1] I. Kolař, P. W. Michor, J. Slovák, Natural Operations In Differential Geometry, Springer Verlag 1993.
• [2] I. Kolař, W. M. Mikulski, Contact elements on fibered manifolds, Czech. Math. J. 53 (128) (2003), 1017-1030.
• [3] J. Kurek, W. M. Mikulski, Liftings of horizontal I-forms to some vector bundle functors on fibered fibered manifolds, Ann. Univ. Mariae Sklodowska Sect. A, 57 (2003), 59-68.
• [4] W. M. Mikulski, The jet prolongations of fibered fibered manifolds and the flow operator, Publ. Math. Debrecen 59 (3-4) (2001), 441-458.
• [5] W. M. Mikulski, J. Tomas, Liftings of projectable projectable vector fields into 1-forms on higher order cotangent bundles over fibered fibered manifolds, Demonstratio Math., 37 (2) (2004), 447-462.
• [6] W. M. Mikulski, J. Tomas, Product preserving bundle functors on fibered fibered manifolds, Colloq. Math. 96 (2003), 17-27.
• [7] W. M. Mikulski, J. Tomas, Natural operators lifting projectable-projectable vector fields to product preserving bundle functors on fibered fibered manifolds, Demonstratio Math., 37 (3) (2004), 697-707.
• [8] R. Wolak, On transverse structures on foliations, Suppl. Rend. Circolo Mat. Palermo 9 (1985), 227-243.