On lifts of linear tensor fields to Weil bundles

Autores/as

  • Ezekiel Kilanta Department of Mathematics and Computer Science, Faculty of Science University of Ngaoundéré, PO.BOX 454 Ngaoundéré, Cameroon
  • Achille Ntyam Department of Mathematics, Higher Teacher Training college University of Yaoundé 1, PO.BOX 47 Yaoundé, Cameroon

DOI:

https://doi.org/10.17398/

Palabras clave:

Double vector bundle, local triviality, duality, linear section, Weil bundle functor, lift

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.

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Referencias

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, 1989.

A. Coste, P. Dazord, A. Weinstein, “Groupoı̈des symplectiques”, Publ. Dép. Math. Nouvelle Sér. A, 87-2, Université Claude-Bernard, Département de Mathématiques, Lyon, 1987.

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 Del Carpio.pdf.

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), 1 – 41.

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 – 118.

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, Polish Academy of Sciences, Institute of Mathematics, Warsaw, 2016, 131 – 166.

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 Press, Cambridge, 2005.

A. Morimoto, Lifting of some types of tensor fields and connections to tangent bundles of pr -velocities, Nagoya Math. J. 40 (1970), 13 – 31.

A. Ntyam, G.F. Wankap Nono, B. Ndombol, On lifts of some projectable vector fields associated to a product preserving gauge bundle functor on vector bundles, Arch. Math. (Brno) 50 (3) (2014), 161 – 169.

J. Pradines, “Fibrés vectoriels doubles et calcul des jets non holonomes”, Esquisses Math., 29, Université d’Amiens, U.E.R. de Mathématiques, Amiens, 1977.

A. Weil, Théorie des points proches sur les variétés différentiables, in ”Géométrie différentielle. Colloques Internationaux du Centre National de la Recherche Scientifique, Strasbourg, 1953” (CNRS, Paris, 1953), 111 – 117.

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Publicado

2025-05-30

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On lifts of linear tensor fields to Weil bundles. (2025). Extracta Mathematicae. https://doi.org/10.17398/