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Let \(\mathcal{M} f_m\) be the category of \(m\)-dimensional manifolds and local diffeomorphisms and let \(T\) be the tangent functor on \(\mathcal{M} f_m\). Let \(\mathcal{V}\) be the category of real vector spaces and linear maps and let \(\mathcal{V}_m\) be the category of \(m\)-dimensional real vector spaces and linear isomorphisms. We characterize all regular covariant functors \(F:\mathcal{V}_m\to\mathcal{V}\) admitting \(\mathcal{M} f_m\)-natural operators \(\tilde J\) transforming classical linear connections \(\nabla\) on \(m\)-dimensional manifolds \(M\) into almost complex structures \(\tilde J(\nabla)\) on \(F(T)M=\bigcup_{x\in M}F(T_xM)\).
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2017
online
2017-06-30
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autor
Bibliografia
- Dombrowski, P., On the geometry of the tangent bundles, J. Reine Angew. Math. 210 (1962), 73-88.
- Kobayashi, S., Nomizu, K., Foundations of Differential Geometry. Vol. I, J. Wiley-Interscience, New York–London, 1963.
- Kolar, I., Michor, P. W., Slovak, J., Natural Operations in Differential Geometry,
- Springer-Verlag, Berlin, 1993.
- Kurek, J., Mikulski, W. M., On lifting of connections to Weil bundles, Ann. Polon. Math. 103 (3) (2012), 319-324.
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bwmeta1.element.ojs-doi-10_17951_a_2017_71_1_55