On almost complex structures from classical linear connections

Jan Kurek, Włodzimierz M. Mikulski

Abstract


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

Keywords


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

Full Text:

PDF

References


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.




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

Refbacks

  • There are currently no refbacks.


Copyright (c) 2017 Jan Kurek, Włodzimierz M. Mikulski