Geodesic
Metrization problem for linear connections and holonomy algebras
Archivum mathematicum, Tome 44 (2008) no. 5, pp. 511-521.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We contribute to the following: given a manifold endowed with a linear connection, decide whether the connection arises from some metric tensor. Compatibility condition for a metric is given by a system of ordinary differential equations. Our aim is to emphasize the role of holonomy algebra in comparison with certain more classical approaches, and propose a possible application in the Calculus of Variations (for a particular type of second order system of ODE’s, which define geodesics of a linear connection, components of a metric compatible with the connection play the role of variational multipliers).
Classification : 53B05, 53B20
Keywords: manifold; linear connection; pseudo-Riemannian metric; holonomy group; holonomy algebra 
@article{ARM_2008__44_5_a11,
     author = {Van\v{z}urov\'a, Alena},
     title = {Metrization problem for linear connections and holonomy algebras},
     journal = {Archivum mathematicum},
     pages = {511--521},
     publisher = {mathdoc},
     volume = {44},
     number = {5},
     year = {2008},
     mrnumber = {2501581},
     zbl = {1212.53021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2008__44_5_a11/}
}
TY  - JOUR
AU  - Vanžurová, Alena
TI  - Metrization problem for linear connections and holonomy algebras
JO  - Archivum mathematicum
PY  - 2008
SP  - 511
EP  - 521
VL  - 44
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ARM_2008__44_5_a11/
LA  - en
ID  - ARM_2008__44_5_a11
ER  - 
%0 Journal Article
%A Vanžurová, Alena
%T Metrization problem for linear connections and holonomy algebras
%J Archivum mathematicum
%D 2008
%P 511-521
%V 44
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ARM_2008__44_5_a11/
%G en
%F ARM_2008__44_5_a11
Vanžurová, Alena. Metrization problem for linear connections and holonomy algebras. Archivum mathematicum, Tome 44 (2008) no. 5, pp. 511-521. http://geodesic.mathdoc.fr/item/ARM_2008__44_5_a11/