On lifts of linear tensor fields to Weil bundles

• Ezekiel Kilanta ^[1] ; Achille 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. 40, Nº 1, 2025, págs. 57-90
• Idioma: inglés
• DOI: 10.17398/2605-5686.40.1.57
• Enlaces
  • Texto completo (pdf)
• Resumen

  • In this paper, we generalize for an arbitrary double vector bundle, some results on linear tensor fields. Moreover we study some properties of their lifts with respect to a product preserving bundle functor

• Referencias bibliográficas
  • H. Bursztyn, A. Cabrera, C. Ortiz, Linear and multiplicative 2-forms, Lett. Math. Phys. 90 (1-3) (2009), 59 – 83.
  • H. Bursztyn, A. Cabrera, Multiplicative forms at the infinitesimal level, Math. Ann. 353 (3) (2012), 663 – 705.
  • L.A. Cordero, C.T.J. Dodson, M. de León, “Differential geometry of frame bundles”, Math. Appl. 47, Kluwer Academic Publishers, Dordrecht,...
  • A. Coste, P. Dazord, A. Weinstein, “Groupoı̈des symplectiques”, Publ. Dép. Math. Nouvelle Sér. A, 87-2, Université Claude-Bernard, Département...
  • T.J. Courant, Dirac Manifolds, Trans. Amer. Math. Soc. 319 (1990), 631 – 661.
  • F. Del Carpio-Marek, “Geometric structures on degree 2 manifolds”, PhD thesis, IMPA, Rio de Janeiro, 2015; available at http://impa.br/wp-content/uploads/2017/05/Fernando...
  • J. Dieudonné, “Eléments d’analyse, tomes 1, 2, 3, 4”, Gauthier-Villars, Paris, 1971.
  • D.J. Eck, Product-preserving functors on smooth manifolds, J. Pure Appl. Algebra 42 (2) (1986), 133 – 140.
  • J. Gancarzewicz, W. Mikulski, Z. Pogoda, Lifts of some tensor fields and connections to product preserving functors, Nagoya Math. J. 135 (1994),...
  • J. Grabowski, M. Rotkiewicz, Higher vector bundles and multi-graded symplectic manifolds, J. Geom. Phys. 59 (9) (2009), 1285 – 1305.
  • E. Hinamari Mang-Massou, A. Ntyam, On lifts of symplectic vector bundles and connections to Weil bundles, Extracta Math. 39 (1) (2024), 97...
  • I. Kolář, Covariant approach to natural transformations of Weil functors, Comment. Math. Univ. Carolin. 27 (4) (1986), 723 – 729.
  • I. Kolář, P.W. Michor, J. Slovák, “Natural operations in differential geometry”, Springer-Verlag, Berlin, 1993.
  • K. Konieczna, P. Urbański, Double vector bundles and duality, Arch. Math. (Brno) 35 (1999), 59 – 95.
  • Y. Kosmann-Scharzbach, Multiplicativity, from Lie groups to generalized geometry, in “Geometry of jets and fields”, Banach Center Publ., 110,...
  • K.C.H. Mackenzie, On symplectic double groupoids and the duality of Poisson groupoids, Internat. J. Math. 10 (4) (1999), 435 – 456.
  • K.C.H. Mackenzie, “General theory of Lie groupoids and Lie algebroids”, London Math. Soc. Lecture Notes Series, 213, Cambridge University...
  • A. Morimoto, Lifting of some types of tensor fields and connections to tangent bundles of pr -velocities, Nagoya Math. J. 40 (1970), 13 –...
  • A. Ntyam, G.F. Wankap Nono, B. Ndombol, On lifts of some projectable vector fields associated to a product preserving gauge bundle functor...
  • J. Pradines, “Fibrés vectoriels doubles et calcul des jets non holonomes”, Esquisses Math., 29, Université d’Amiens, U.E.R. de Mathématiques,...
  • A. Weil, Théorie des points proches sur les variétés différentiables, in ”Géométrie différentielle. Colloques Internationaux du Centre National...