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On K-Jet Field Approximations to Geodesic Deviation Equations

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On K-Jet Field Approximations to Geodesic Deviation Equations. / Gratus, Jonathan; Gallego Torrome, Ricardo.
In: International Journal of Geometric Methods in Modern Physics, Vol. 15, No. 12, 1850199, 2018.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Gratus, J & Gallego Torrome, R 2018, 'On K-Jet Field Approximations to Geodesic Deviation Equations', International Journal of Geometric Methods in Modern Physics, vol. 15, no. 12, 1850199. https://doi.org/10.1142/S0219887818501992

APA

Gratus, J., & Gallego Torrome, R. (2018). On K-Jet Field Approximations to Geodesic Deviation Equations. International Journal of Geometric Methods in Modern Physics, 15(12), Article 1850199. https://doi.org/10.1142/S0219887818501992

Vancouver

Gratus J, Gallego Torrome R. On K-Jet Field Approximations to Geodesic Deviation Equations. International Journal of Geometric Methods in Modern Physics. 2018;15(12):1850199. Epub 2018 Oct 1. doi: 10.1142/S0219887818501992

Author

Gratus, Jonathan ; Gallego Torrome, Ricardo. / On K-Jet Field Approximations to Geodesic Deviation Equations. In: International Journal of Geometric Methods in Modern Physics. 2018 ; Vol. 15, No. 12.

Bibtex

@article{8bac5e77120d4564b033837b82a724e8,
title = "On K-Jet Field Approximations to Geodesic Deviation Equations",
abstract = "Let M be a smooth manifold and S a semi-spray defined on a sub-bundle C of the tangent bundle TM . In this work it is proved that the only non-trivial k-jet approximation to the exact geodesic deviation equation of S, linear on the deviation functions and invariant under an specific class of local coordinate transformations is the Jacobi equation. However, if the linearity property on the dependence in the deviation functions is not imposed, then there are differential equations whose solutions admit k-jet approximations and are invariant under arbitrary coordinate transformations. As an example of higher order geodesic deviation equations we study the first and second order geodesic deviation equations for a Finsler spray.",
author = "Jonathan Gratus and {Gallego Torrome}, Ricardo",
year = "2018",
doi = "10.1142/S0219887818501992",
language = "English",
volume = "15",
journal = "International Journal of Geometric Methods in Modern Physics",
issn = "0219-8878",
publisher = "World Scientific",
number = "12",

}

RIS

TY - JOUR

T1 - On K-Jet Field Approximations to Geodesic Deviation Equations

AU - Gratus, Jonathan

AU - Gallego Torrome, Ricardo

PY - 2018

Y1 - 2018

N2 - Let M be a smooth manifold and S a semi-spray defined on a sub-bundle C of the tangent bundle TM . In this work it is proved that the only non-trivial k-jet approximation to the exact geodesic deviation equation of S, linear on the deviation functions and invariant under an specific class of local coordinate transformations is the Jacobi equation. However, if the linearity property on the dependence in the deviation functions is not imposed, then there are differential equations whose solutions admit k-jet approximations and are invariant under arbitrary coordinate transformations. As an example of higher order geodesic deviation equations we study the first and second order geodesic deviation equations for a Finsler spray.

AB - Let M be a smooth manifold and S a semi-spray defined on a sub-bundle C of the tangent bundle TM . In this work it is proved that the only non-trivial k-jet approximation to the exact geodesic deviation equation of S, linear on the deviation functions and invariant under an specific class of local coordinate transformations is the Jacobi equation. However, if the linearity property on the dependence in the deviation functions is not imposed, then there are differential equations whose solutions admit k-jet approximations and are invariant under arbitrary coordinate transformations. As an example of higher order geodesic deviation equations we study the first and second order geodesic deviation equations for a Finsler spray.

U2 - 10.1142/S0219887818501992

DO - 10.1142/S0219887818501992

M3 - Journal article

VL - 15

JO - International Journal of Geometric Methods in Modern Physics

JF - International Journal of Geometric Methods in Modern Physics

SN - 0219-8878

IS - 12

M1 - 1850199

ER -