Prolongations of G-structures related to Weil bundles and some applications

• P.M. Kouotchop Wamba ^[2] ; Georgy F. Wankap Nono ^[1] ; A. Ntyam ^[2]
  1. [1] University of Ngaoundéré

     University of Ngaoundéré

     Camerún

     
  2. [2] Department of Mathematics, Higher Teacher Training college University of Yaoundé 1, PO.BOX 47 Yaoundé, Cameroon
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 37, Nº 1, 2022, págs. 111-138
• Idioma: inglés
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• Resumen

  • Let M be a smooth manifold of dimension m ≥ 1 and P be a G-structure on M , where G is a Lie subgroup of linear group GL(m). In [8], it has been defined the prolongations of G-structures related to tangent functor of higher order and some properties have been established. The aim of this paper is to generalize these prolongations to a Weil bundles. More precisely, we study the prolongations of G-structures on a manifold M , to its Weil bundle TAM (A is a Weil algebra) and we establish some properties. In particular, we characterize the canonical tensor fields induced by the A-prolongation of some classical G-structures.