On almost polynomial structures from classical linear connections

Anna Bednarska

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. Let \(w\) be a polynomial in one variable with real coefficients. We describe all regular covariant functors \(F\colon \mathcal{V}_m\to\mathcal{V}\) admitting \(\mathcal{M}f_m\)-natural operators \(\tilde{P}\) transforming classical linear connections \(\nabla\) on \(m\)-dimensional manifolds \(M\) into almost polynomial \(w\)-structures  \(\tilde{P}(\nabla)\) on \(F(T)M=\bigcup_{x\in M}F(T_xM)\).


Keywords


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

Full Text:

PDF

References


Kaneyuki, S., Kozai, M., Paracomplex structures and affine symmetric spaces, Tokyo J. Math. 8 (1) (1985), 81-98.

Kobayashi, S., Nomizu, K., Foundations of Differential Geometry. Vol I, Interscience Publisher, 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.

Kurek, J., Mikulski, W. M., On almost complex structures from classical linear connections, Ann. Univ. Mariae Curie-Skłodowska Sect. A, 71 (1) (2017), 55-60.

Libermann, P., Sur les structures presque paracomplexes, C. R. Acad. Sci. Paris 234 (1952), 2517-2519.

Libermann, P., Sur le probleme d’equivalence de certaines structures infinitesimales, Ann. Mat. Pura Appl. 36 (1954), 27-120.




DOI: http://dx.doi.org/10.17951/a.2018.72.1.13-18
Data publikacji: 2018-06-25 09:04:03
Data złożenia artykułu: 2018-06-24 16:29:31


Statistics

Total abstract view - 300
Downloads (from 2020-06-17) - PDF - 24

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2018 Anna Bednarska