# Geometry of second-order connections and ordinary differential equations

Mathematica Bohemica (1995)

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

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topVondra, 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 -

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