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

Authors

  • P.M. Kouotchop Wamba Department of Mathematics, Higher Teacher Training college University of Yaoundé 1, PO.BOX 47 Yaoundé, Cameroon
  • G.F. Wankap Nono Department of Mathematics and Computer Science, Faculty of Science University of Ngaoundéré, PO.BOX 454 Ngaoundéré, Cameroon
  • A. Ntyam Department of Mathematics, Higher Teacher Training college University of Yaoundé 1, PO.BOX 47 Yaoundé, Cameroon

DOI:

https://doi.org/10.17398/2605-5686.37.1.111

Keywords:

G-structures, Weil-Frobenius algebras, Weil functors, gauge functors and natural transformations

Abstract

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.

Downloads

Download data is not yet available.

References

D. Bernard, Sur la géométrie differentielle des G-structures, Ann. Inst. Fourier (Grenoble) 10 (1960), 151 – 270.

A. Cabras, I. Kolar, Prolongation of tangent valued forms to Weil bundles, Arch. Math. (Brno) 31 (2) (1995), 139 – 145.

J. Debecki, Linear natural operators lifting p-vectors to tensors of type (q, 0) on Weil bundles, Czechoslovak Math. J. 66 (2) (2016), 511 – 525.

M. Doupovec, M. Kures, Some geometric constructions on Frobenius Weil bundles, Differential Geom. Appl. 35 (2014), 143 – 149.

J. Gancarzewicz, W. Mikulski, Z. Pogoda, Lifts of some tensor fields and connections to product preserving functors, Nagoya Math. J. 135 (1994), 1 – 41.

I. Kolar, On the geometry of Weil bundles, Differential Geom. Appl. 35 (2014), 136 – 142.

I. Kolar, Covariant approach to natural transformations of Weil functors, Comment. Math. Univ. Carolin. 27 (4) (1986), 723 – 729.

I. Kolar, P. Michor, J. Slovak, “Natural Operations in Differential Geometry”, Springer-Verlag, Berlin, 1993.

P.M. Kouotchop Wamba, A. Ntyam, Prolongations of Dirac structures related to Weil bundles, Lobachevskii J. Math. 35 (2014), 106 – 121.

P.M. Kouotchop Wamba, A. Mba, Characterization of some natural transformations between the bundle functors T A ◦T ∗ and T ∗ ◦T A on Mfm, IMHOTEP J. Afr. Math. Pures Appl. 3 (2018), 21 – 32.

M. Kures, W. Mikulski, Lifting of linear vector fields to product preserving gauge bundle functors on vector bundles, Lobachevskii J. Math. 12 (2003), 51 – 61.

A. Morimoto, Prolongations of G-structure to tangent bundles of higher order, Nagoya Math. J. 38 (1970), 153 – 179.

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

Downloads

Published

2022-06-01

Issue

Vol. 37 No. 1 (2022)

Section

Differential Geometry

How to Cite

Prolongations of G-structures related to Weil bundles and some applications. (2022). Extracta Mathematicae, 37(1), 111-138. https://doi.org/10.17398/2605-5686.37.1.111