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Lifts of some tensor fields and connections to product preserving functors

Published online by Cambridge University Press:  22 January 2016

Jacek Gancarzewicz ,
Włodzimierz Mikulski  and
Zdzisław Pogoda
Jacek Gancarzewicz
Affiliation:
Instytut Matematyki UJ, ul. Reymonta 4, 30-059 Kraków, Poland e-mail:(JG) [email protected], (WM) [email protected], (ZP) [email protected]
Włodzimierz Mikulski
Affiliation:
Instytut Matematyki UJ, ul. Reymonta 4, 30-059 Kraków, Poland e-mail:(JG) [email protected], (WM) [email protected], (ZP) [email protected]
Zdzisław Pogoda
Affiliation:
Instytut Matematyki UJ, ul. Reymonta 4, 30-059 Kraków, Poland e-mail:(JG) [email protected], (WM) [email protected], (ZP) [email protected]
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In this paper we define some lifts of tensor fields of types (1, k) and (0, k) as well as connections to a product preserving functor . We study algebraic properties of introduced lifts and we apply these lifts to prolongation of geometric structures from a manifold M to (M). In particular cases of the tangent bundle of pr -velocities and the tangent bundle of infinitesimal near points our constructions contain all constructions due to Morimoto (see [20]-[23]). In the cases of the tangent bundle our definitions coincide with the definitions of Yano and Kobayashi (see [31]). To construct our lifts and to study its properties we use only general properties of product preserving functors. All lifts verify so-called the naturality condition. It means that for a smooth mapping φ:M → N and for two φ-related geometric objects defined on M and N its lifts to (M) and (N) respectively are (φ)-related. We explain later the term φ-related for considered geometric objects.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 135 , September 1994 , pp. 1 - 41
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1994

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