Geometry of second-order connections and ordinary differential equations

Alexandr Vondra

Mathematica Bohemica (1995)

  • Volume: 120, Issue: 2, page 145-167
  • ISSN: 0862-7959

Abstract

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The geometry of second-order systems of ordinary differential equations represented by 2 -connections on the trivial bundle error ℝ × M → ℝ is studied. The formalism used, being completely utilizable within the framework of more general situations (partial equations), turns out to be of interest in confrontation with a traditional approach (semisprays), moreover, it amounts to certain new ideas and results. The paper is aimed at discussion on the interrelations between all types of connections having to do with integral sections (geodesics), integrals and symmetries of the equations studied.

How to cite

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Vondra, Alexandr. "Geometry of second-order connections and ordinary differential equations." Mathematica Bohemica 120.2 (1995): 145-167. <http://eudml.org/doc/247793>.

@article{Vondra1995,
abstract = {The geometry of second-order systems of ordinary differential equations represented by $2$-connections on the trivial bundle $\operatorname\{pr_1\} \mathbb \{R\}\times M\rightarrow \mathbb \{R\}$ is studied. The formalism used, being completely utilizable within the framework of more general situations (partial equations), turns out to be of interest in confrontation with a traditional approach (semisprays), moreover, it amounts to certain new ideas and results. The paper is aimed at discussion on the interrelations between all types of connections having to do with integral sections (geodesics), integrals and symmetries of the equations studied.},
author = {Vondra, Alexandr},
journal = {Mathematica Bohemica},
keywords = {geometry of second-order systems of ordinary differential equations; $2$- connections; connection; semispray; differential equation; integral; symmetry; geometry of second-order systems of ordinary differential equations; 2- connections},
language = {eng},
number = {2},
pages = {145-167},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Geometry of second-order connections and ordinary differential equations},
url = {http://eudml.org/doc/247793},
volume = {120},
year = {1995},
}

TY - JOUR
AU - Vondra, Alexandr
TI - Geometry of second-order connections and ordinary differential equations
JO - Mathematica Bohemica
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 120
IS - 2
SP - 145
EP - 167
AB - The geometry of second-order systems of ordinary differential equations represented by $2$-connections on the trivial bundle $\operatorname{pr_1} \mathbb {R}\times M\rightarrow \mathbb {R}$ is studied. The formalism used, being completely utilizable within the framework of more general situations (partial equations), turns out to be of interest in confrontation with a traditional approach (semisprays), moreover, it amounts to certain new ideas and results. The paper is aimed at discussion on the interrelations between all types of connections having to do with integral sections (geodesics), integrals and symmetries of the equations studied.
LA - eng
KW - geometry of second-order systems of ordinary differential equations; $2$- connections; connection; semispray; differential equation; integral; symmetry; geometry of second-order systems of ordinary differential equations; 2- connections
UR - http://eudml.org/doc/247793
ER -

References

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