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
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.
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页码:1277 / 1290
页数:14
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