Natural affinors and torsion of connections on Weil like functors on double vector bundles

Miroslav Doupovec, Jan Kurek, Włodzimierz Mikulski

Abstract


We describe completely all natural affinors on product preserving gauge bundle functors  on double vector bundles. Next, we study torsion of double-linear connections.

Keywords


Double vector bundle; product preserving gauge bundle functor; natural affinor; torsion of double-linear connection

Full Text:

PDF

References


Chen, Z., Liu, Z. J., Scheng, Y. H., On double vector bundles, Acta Math. Sinica (E-S) 30 (2014), 1655–1673.

Doupovec, M., Kolar, I., Natural affinors on time-dependent Weil bundles, Arch. Math. (Brno) 27 (1991), 205–209.

Gancarzewicz, J., Kolar, I., Natural affinors on the extended r-th order tangent bundles, Suppl. Rend. Circ. Mat. Palermo 30 (1993), 95–100.

Janyska, J., Natural operations with projectable tangent valued forms, Ann. Mat. Pura Appl. CLIX (1991), 171–187.

Kolar, I., Michor, P. W., Slovak, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993.

Kolar, I., Modugno, M., Torsions of connections on some natural bundles, Differential Geom. Appl. 2 (1992), 1–16.

Konieczna, K., Urbański, P., Double vector bundles and duality, Arch. Math. Brno 35 (1) (1999), 59–95.

Kurek, J., Natural affinors on higher order cotangent bundle, Arch. Math. Brno 28 (1992), 175–180.

Mackenzie, K. C. H., General Theory of Lie Groupoids and Lie Algebroids, Cambridge University Press, Cambridge, 2015.

Mikulski, W. M., Lifting double linear vector fields to Weil like functors on double vector bundles, Math. Nachr. 292 (9) (2019), 2092–2100.

Mikulski, W. M., Complete lifting of double-linear semi-basic tangent-valued forms to Weil like functors on double vector bundles, Rev. Un. Math. Argentina 62 (2) (2021), 351–363.

Pradines, J., Geometrie differentielle au-dessus d’un groupoide, C. R. Acad. Sci. Paris Ser. A–B 266 (1968) (A): 1194–1196.

Tulczyjew, W. M., Geometric Formulations of Physical Theories, Bibliopolis, Napoli, 1989.




DOI: http://dx.doi.org/10.17951/a.2022.76.2.1-13
Date of publication: 2023-03-13 22:27:58
Date of submission: 2023-03-12 16:50:45


Statistics


Total abstract view - 473
Downloads (from 2020-06-17) - PDF - 315

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2022 Miroslav Doupovec, Jan Kurek, Włodzimierz Mikulski