Sprays and homogeneous connections on 𝐑 × 𝑇𝑀

Alexandr Vondra

Archivum Mathematicum (1992)

  • Volume: 028, Issue: 3-4, page 163-173
  • ISSN: 0044-8753

Abstract

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The homogeneity properties of two different families of geometric objects playing a crutial role in the non-autonomous first-order dynamics - semisprays and dynamical connections on R × T M - are studied. A natural correspondence between sprays and a special class of homogeneous connections is presented.

How to cite

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Vondra, Alexandr. "Sprays and homogeneous connections on ${\bf R}\times {\it TM}$." Archivum Mathematicum 028.3-4 (1992): 163-173. <http://eudml.org/doc/247348>.

@article{Vondra1992,
abstract = {The homogeneity properties of two different families of geometric objects playing a crutial role in the non-autonomous first-order dynamics - semisprays and dynamical connections on $R\times TM$ - are studied. A natural correspondence between sprays and a special class of homogeneous connections is presented.},
author = {Vondra, Alexandr},
journal = {Archivum Mathematicum},
keywords = {semispray; connection; path; torsion; tension; spray; homogeneous dynamical connection; homogeneous dynamical connections; sprays},
language = {eng},
number = {3-4},
pages = {163-173},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Sprays and homogeneous connections on $\{\bf R\}\times \{\it TM\}$},
url = {http://eudml.org/doc/247348},
volume = {028},
year = {1992},
}

TY - JOUR
AU - Vondra, Alexandr
TI - Sprays and homogeneous connections on ${\bf R}\times {\it TM}$
JO - Archivum Mathematicum
PY - 1992
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 028
IS - 3-4
SP - 163
EP - 173
AB - The homogeneity properties of two different families of geometric objects playing a crutial role in the non-autonomous first-order dynamics - semisprays and dynamical connections on $R\times TM$ - are studied. A natural correspondence between sprays and a special class of homogeneous connections is presented.
LA - eng
KW - semispray; connection; path; torsion; tension; spray; homogeneous dynamical connection; homogeneous dynamical connections; sprays
UR - http://eudml.org/doc/247348
ER -

References

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  13. Torsion and Ricci tensor for non-linear connections, (to appear). 
  14. The Geometry of Jet Bundles, London Mathematical Society Lecture Note Series 142 (1989), Cambridge University Press. (1989) Zbl0665.58002MR0989588
  15. Lectures on Differential Geometry, Prentice-Hall, 1965. (1965) MR0193578
  16. Second-order equation fields and the inverse problem of Lagrangian dynamics, J. Math. Phys. 28 (12) (1987), 2851-2857. (1987) Zbl0638.70013MR0917639
  17. On some connections related to the geometry of regular higher-order dynamics, (preprint, 1990). 
  18. Semisprays, connections and regular equations in higher order mechanics, Proc. Conf. Diff. Geom. and Its Appl. (19891990), World Scientific, Brno Singapore, 276-287. (19891990) MR1062030

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