# Tangent Lie algebras to the holonomy group of a Finsler manifold

Communications in Mathematics (2011)

- Volume: 19, Issue: 2, page 137-147
- ISSN: 1804-1388

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topMuzsnay, Zoltán, and Nagy, Péter T.. "Tangent Lie algebras to the holonomy group of a Finsler manifold." Communications in Mathematics 19.2 (2011): 137-147. <http://eudml.org/doc/246536>.

@article{Muzsnay2011,

abstract = {Our goal in this paper is to make an attempt to find the largest Lie algebra of vector fields on the indicatrix such that all its elements are tangent to the holonomy group of a Finsler manifold. First, we introduce the notion of the curvature algebra, generated by curvature vector fields, then we define the infinitesimal holonomy algebra by the smallest Lie algebra of vector fields on an indicatrix, containing the curvature vector fields and their horizontal covariant derivatives with respect to the Berwald connection. At the end we introduce conjugates of infinitesimal holonomy algebras by parallel translations with respect to the Berwald connection. We prove that this holonomy algebra is tangent to the holonomy group.},

author = {Muzsnay, Zoltán, Nagy, Péter T.},

journal = {Communications in Mathematics},

keywords = {higher order field theories; boundary terms; tangent Lie algebra; the holonomy group; Finsler manifold},

language = {eng},

number = {2},

pages = {137-147},

publisher = {University of Ostrava},

title = {Tangent Lie algebras to the holonomy group of a Finsler manifold},

url = {http://eudml.org/doc/246536},

volume = {19},

year = {2011},

}

TY - JOUR

AU - Muzsnay, Zoltán

AU - Nagy, Péter T.

TI - Tangent Lie algebras to the holonomy group of a Finsler manifold

JO - Communications in Mathematics

PY - 2011

PB - University of Ostrava

VL - 19

IS - 2

SP - 137

EP - 147

AB - Our goal in this paper is to make an attempt to find the largest Lie algebra of vector fields on the indicatrix such that all its elements are tangent to the holonomy group of a Finsler manifold. First, we introduce the notion of the curvature algebra, generated by curvature vector fields, then we define the infinitesimal holonomy algebra by the smallest Lie algebra of vector fields on an indicatrix, containing the curvature vector fields and their horizontal covariant derivatives with respect to the Berwald connection. At the end we introduce conjugates of infinitesimal holonomy algebras by parallel translations with respect to the Berwald connection. We prove that this holonomy algebra is tangent to the holonomy group.

LA - eng

KW - higher order field theories; boundary terms; tangent Lie algebra; the holonomy group; Finsler manifold

UR - http://eudml.org/doc/246536

ER -

## References

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