Description of jet like functors on vector bundles by means of module bundle functors on the bases

被引：0

作者：

Doupovec, Miroslav ^{[1
]}

Kurek, Jan ^{[2
]}

Mikulski, Wlodzimierz M. ^{[3
]}

机构：

[1] Brno Univ Technol, Inst Math, FSI VUT Brno, Technicka 2, Brno, Czech Republic

[2] Marie Curie Sklodowska Univ, Inst Math, Pl Marii Curie Sklodowskiej 1, Lublin, Poland

[3] Jagiellonian Univ, Inst Math, ul Lojasiewicza 6, PL-30348 Krakow, Poland

来源：

FILOMAT | 2024年 / 38卷 / 01期

关键词：

(gauge) bundle functor; vector bundle; module bundle; jet;

D O I：

10.2298/FIL2401241D

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let C be an admissible category over manifolds and VBC be the category of vector bundles with bases being C-objects and vector bundle maps with base maps being C-maps. Assume that any C-morphism is a local isomorphism. We describe all jet like functors (i.e. fiber product preserving gauge bundle functors) of order r on VBC by means of Jr(-, R)-module bundle functors on C. Then we describe all jet like functors of vertical type of order r on VBC by means of vector bundle functors on C of order r. As an application we classify jet like functors of some type on VBm. Finally, we determine all natural Jr(M, R)-module bundle structures on the vector bundles JrE -* M and JrvE -* M, where E -* M is a vector bundle with m-dimensional basis and m >= 2.

引用

页码：241 / 260

页数：20