Connections of Higher Order and Product Preserving Functors

Authors: Gancarzewicz J.¹; Rahmani N.²; Salgado M.³

Source: Czechoslovak Mathematical Journal, Volume 52, Number 4, December 2002 , pp. 889-896(8)

Publisher: Springer

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Abstract:

In this paper we consider a product preserving functor <IMG SRC="http://images.ingentaselect.com/absimages/klu/00114642/klu_cmaj_2002_52_4_426289h.1.gif" ALT="\cal F" TEXT="a mathematical formula"> of order r and a connection Ggr

of order r on a manifold M. We introduce horizontal lifts of tensor fields and linear connections from M to <IMG SRC="http://images.ingentaselect.com/absimages/klu/00114642/klu_cmaj_2002_52_4_426289h.2.gif" ALT="\cal F(M)" TEXT="a mathematical formula"> with respect to Ggr

. Our definitions and results generalize the particular cases of the tangent bundle and the tangent bundle of higher order.

Keywords: connections of higher order; product preserving functors; lifts of tensors and connections

Document Type: Research article

DOI: http://dx.doi.org/10.1023/B:CMAJ.0000027242.32639.5c

Affiliations: 1: Instytut Matematyki UJ, ul. Reymonta 4, 30-059 Kraków, Pologne, Email: gancarze@im.uj.edu.pl 2: Institute de Mathematiques Appliques et Informatique, USTO, Oran, Algérie 3: Departamento de Xeometría e Topoloxía, Universidade de Santiago de Compostela, Espagne, Email: modesto@zmat.usc.es

Publication date: 2002-12-01