On almost complex structures from classical linear connections

Jan Kurek, Włodzimierz M. Mikulski


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 \(F(T)M=\bigcup_{x\in M}F(T_xM)\).


Classical linear connection; almost complex structure; Weil bundle; natural operator

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DOI: http://dx.doi.org/10.17951/a.2017.71.1.55
Data publikacji: 2017-06-30 17:33:55
Data złożenia artykułu: 2017-06-30 12:18:29


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