On lifting of connections to Weil bundles

Jan Kurek; Włodzimierz M. Mikulski

Annales Polonici Mathematici, Tome 105 (2012), p. 319-324 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove that the problem of finding all $ℳ f_{m}$ -natural operators $B : Q ⟿ Q T^{A}$ lifting classical linear connections ∇ on m-manifolds M to classical linear connections $B_{M} (\nabla)$ on the Weil bundle $T^{A} M$ corresponding to a p-dimensional (over ℝ) Weil algebra A is equivalent to the one of finding all $ℳ f_{m}$ -natural operators $C : Q ⟿ (T ¹_{p - 1}, T * \otimes T * \otimes T)$ transforming classical linear connections ∇ on m-manifolds M into base-preserving fibred maps $C_{M} (\nabla) : T ¹_{p - 1} M = ⨁_{M}^{p - 1} T M \to T * M \otimes T * M \otimes T M$ .

Publié le : 2012-01-01

Zbl 1245.58003

EUDML-ID : urn:eudml:doc:280351

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     title = {On lifting of connections to Weil bundles},
     journal = {Annales Polonici Mathematici},
     volume = {105},
     year = {2012},
     pages = {319-324},
     zbl = {1245.58003},
     language = {en},
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Jan Kurek; Włodzimierz M. Mikulski. On lifting of connections to Weil bundles. Annales Polonici Mathematici, Tome 105 (2012) pp. 319-324. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap103-3-7/