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Natural Affinors On Higher Order Cotangent Bundle

By Jan Kur Ek

Abstract

. All natural affinors on the r-th order cotangent bundle T r M are determined. Basic affinors of this type are the identity affinor id of TT r M and the s-th power affinors Q s M : TT r M ! V T r M with s = 1; : : : ; r defined by the s-th power transformations A r;r s of T r M . An arbitrary natural affinor is a linear combination of the basic ones. Recently, Kol'ar and Modugno have determined all natural affinors on cotangent bundle T M , which constitute a 2 parameter family linearly generated by the identity of TT M and by a natural affinor QM : TT M ! V T M , [1]. In this paper, we determine all natural affinors on the r-th order cotangent bundle T r M . We deduce that all natural affinors on the r-th cotangent bundle T r M form a (r + 1)-parameter family linearly generated by the identity affinor id of TT r M and by the s-th power natural affinors Q s M : TT r M ! V T r M with s = 1; : : : ; r defined by the s-th power natural tr..

Year: 2007
OAI identifier: oai:CiteSeerX.psu:10.1.1.31.5200
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