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Keywords:
jet; Weil bundle; Grassmann manifold
jet; Weil bundle; Grassmann manifold
Summary:
Given a Weil algebra $A$ and a smooth manifold $M$, we prove that the set $J^AM$ of kernels of regular $A$-points of $M$, $\check{M}^A$, has a differentiable manifold structure and $\check{M}^A\longrightarrow J^AM$ is a principal fiber bundle.
References:
[1] Kolář I.: Affine structure on Weil bundles. To appear in Nagoya Math J. MR 1766571 | Zbl 0961.58002
[2] Kolář I., Michor P. W., Slovák J.: Natural operations in differential geometry. Springer-Verlag, New York, 1993. MR 1202431 | Zbl 0782.53013
[3] Muñoz, J, Muriel F. J., and Rodríguez J.: Weil bundles and jet spaces. To appear in Czech. Math. J.
[4] Weil A.: Théorie des points proches sur les variétés différentiables. Colloque de Géometrie Différentielle, C.N.R.S. (1953), 111–117. MR 0061455 | Zbl 0053.24903
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