Prolongations of G-structures related to Weil bundles and some applications
Main Article Content
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.
Metrics
Metrics Loading ...
Article Details
How to Cite
Kouotchop Wamba, P., Wankap Nono, G., & Ntyam, A. (2022). Prolongations of G-structures related to Weil bundles and some applications. Extracta Mathematicae, 37(1), 111-138. https://doi.org/10.17398/2605-5686.37.1.111
Issue
Section
Differential Geometry
References
[1] D. Bernard, Sur la géométrie differentielle des G-structures, Ann. Inst. Fourier (Grenoble) 10 (1960), 151 – 270.
[2] A. Cabras, I. Kolar, Prolongation of tangent valued forms to Weil bundles, Arch. Math. (Brno) 31 (2) (1995), 139 – 145.
[3] 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.
[4] M. Doupovec, M. Kures, Some geometric constructions on Frobenius Weil bundles, Differential Geom. Appl. 35 (2014), 143 – 149.
[5] J. Gancarzewicz, W. Mikulski, Z. Pogoda, Lifts of some tensor fields and connections to product preserving functors, Nagoya Math. J. 135 (1994), 1 – 41.
[6] I. Kolar, On the geometry of Weil bundles, Differential Geom. Appl. 35 (2014), 136 – 142.
[7] I. Kolar, Covariant approach to natural transformations of Weil functors, Comment. Math. Univ. Carolin. 27 (4) (1986), 723 – 729.
[8] I. Kolar, P. Michor, J. Slovak, “Natural Operations in Differential Geometry”, Springer-Verlag, Berlin, 1993.
[9] P.M. Kouotchop Wamba, A. Ntyam, Prolongations of Dirac structures related to Weil bundles, Lobachevskii J. Math. 35 (2014), 106 – 121.
[10] 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.
[11] 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.
[12] A. Morimoto, Prolongations of G-structure to tangent bundles of higher order, Nagoya Math. J. 38 (1970), 153 – 179.
[13] A. Morimoto, Lifting of some types of tensor fields and connections to tangent bundles of pr -velocities, Nagoya Math. J. 40 (1970), 13 – 31.
[2] A. Cabras, I. Kolar, Prolongation of tangent valued forms to Weil bundles, Arch. Math. (Brno) 31 (2) (1995), 139 – 145.
[3] 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.
[4] M. Doupovec, M. Kures, Some geometric constructions on Frobenius Weil bundles, Differential Geom. Appl. 35 (2014), 143 – 149.
[5] J. Gancarzewicz, W. Mikulski, Z. Pogoda, Lifts of some tensor fields and connections to product preserving functors, Nagoya Math. J. 135 (1994), 1 – 41.
[6] I. Kolar, On the geometry of Weil bundles, Differential Geom. Appl. 35 (2014), 136 – 142.
[7] I. Kolar, Covariant approach to natural transformations of Weil functors, Comment. Math. Univ. Carolin. 27 (4) (1986), 723 – 729.
[8] I. Kolar, P. Michor, J. Slovak, “Natural Operations in Differential Geometry”, Springer-Verlag, Berlin, 1993.
[9] P.M. Kouotchop Wamba, A. Ntyam, Prolongations of Dirac structures related to Weil bundles, Lobachevskii J. Math. 35 (2014), 106 – 121.
[10] 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.
[11] 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.
[12] A. Morimoto, Prolongations of G-structure to tangent bundles of higher order, Nagoya Math. J. 38 (1970), 153 – 179.
[13] A. Morimoto, Lifting of some types of tensor fields and connections to tangent bundles of pr -velocities, Nagoya Math. J. 40 (1970), 13 – 31.