Principal bundle structure on jet prolongations of frame bundles

被引：1

作者：

Brajercik, J. ^{[1
]}

Demko, M. ^{[1
]}

Krupka, D. ^{[2
,3
,4
]}

机构：

[1] Univ Presov, Dept Phys Math & Tech, Ul 17 Novembra 1, SK-08116 Presov, Slovakia

[2] Beijing Inst Technol, Sch Math, Beijing 100081, Peoples R China

[3] La Trobe Univ, Dept Math, Melbourne, Vic 3086, Australia

[4] Univ Ostrava, Dept Math, CZ-70103 Ostrava, Czech Republic

来源：

MATHEMATICA SLOVACA | 2014年 / 64卷 / 05期

基金：

美国国家科学基金会;

关键词：

principal bundle; frame bundle; structure group; prolongation; associated bundle;

D O I：

10.2478/s12175-014-0275-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce the structure of a principal bundle on the r-jet prolongation J (r) FX of the frame bundle FX over a manifold X. Our construction reduces the well-known principal prolongation W (r) FX of FX with structure group G (n) (r) . For a structure group of J (r) FX we find a suitable subgroup of G (n) (r) . We also discuss the structure of the associated bundles. We show that the associated action of the structure group of J (r) FX corresponds with the standard actions of differential groups on tensor spaces.

引用

页码：1277 / 1290

页数：14

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