Lifting to the r-frame bundle by means of connections

J. Kurek; W. M. Mikulski

J. Kurek ; W. M. Mikulski

Annales Polonici Mathematici, Tome 98 (2010), p. 63-71 / Harvested from The Polish Digital Mathematics Library

Résumé

Let m and r be natural numbers and let $P^{r} : ℳ f_{m} \to ℱ ℳ$ be the rth order frame bundle functor. Let $F : ℳ f_{m} \to ℱ ℳ$ and $G : ℳ f_{k} \to ℱ ℳ$ be natural bundles, where $k = d i m (P^{r} ℝ^{m})$ . We describe all $ℳ f_{m}$ -natural operators A transforming sections σ of $F M \to M$ and classical linear connections ∇ on M into sections A(σ,∇) of $G (P^{r} M) \to P^{r} M$ . We apply this general classification result to many important natural bundles F and G and obtain many particular classifications.

Publié le : 2010-01-01

Zbl 1193.58001

EUDML-ID : urn:eudml:doc:280755

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     title = {Lifting to the r-frame bundle by means of connections},
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     year = {2010},
     pages = {63-71},
     zbl = {1193.58001},
     language = {en},
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J. Kurek; W. M. Mikulski. Lifting to the r-frame bundle by means of connections. Annales Polonici Mathematici, Tome 98 (2010) pp. 63-71. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap97-1-5/