On the projective Finsler metrizability and the integrability of Rapcsák equation

Tamás Milkovszki; Zoltán Muzsnay

Czechoslovak Mathematical Journal (2017)

  • Volume: 67, Issue: 2, page 469-495
  • ISSN: 0011-4642

Abstract

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A. Rapcsák obtained necessary and sufficient conditions for the projective Finsler metrizability in terms of a second order partial differential system. In this paper we investigate the integrability of the Rapcsák system and the extended Rapcsák system, by using the Spencer version of the Cartan-Kähler theorem. We also consider the extended Rapcsák system completed with the curvature condition. We prove that in the non-isotropic case there is a nontrivial Spencer cohomology group in the sequences determining the 2-acyclicity of the symbol of the corresponding differential operator. Therefore the system is not integrable and higher order obstruction exists.

How to cite

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Milkovszki, Tamás, and Muzsnay, Zoltán. "On the projective Finsler metrizability and the integrability of Rapcsák equation." Czechoslovak Mathematical Journal 67.2 (2017): 469-495. <http://eudml.org/doc/288197>.

@article{Milkovszki2017,
abstract = {A. Rapcsák obtained necessary and sufficient conditions for the projective Finsler metrizability in terms of a second order partial differential system. In this paper we investigate the integrability of the Rapcsák system and the extended Rapcsák system, by using the Spencer version of the Cartan-Kähler theorem. We also consider the extended Rapcsák system completed with the curvature condition. We prove that in the non-isotropic case there is a nontrivial Spencer cohomology group in the sequences determining the 2-acyclicity of the symbol of the corresponding differential operator. Therefore the system is not integrable and higher order obstruction exists.},
author = {Milkovszki, Tamás, Muzsnay, Zoltán},
journal = {Czechoslovak Mathematical Journal},
keywords = {Euler-Lagrange equation; metrizability; projective metrizability; geodesics; spray; formal integrability},
language = {eng},
number = {2},
pages = {469-495},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the projective Finsler metrizability and the integrability of Rapcsák equation},
url = {http://eudml.org/doc/288197},
volume = {67},
year = {2017},
}

TY - JOUR
AU - Milkovszki, Tamás
AU - Muzsnay, Zoltán
TI - On the projective Finsler metrizability and the integrability of Rapcsák equation
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 2
SP - 469
EP - 495
AB - A. Rapcsák obtained necessary and sufficient conditions for the projective Finsler metrizability in terms of a second order partial differential system. In this paper we investigate the integrability of the Rapcsák system and the extended Rapcsák system, by using the Spencer version of the Cartan-Kähler theorem. We also consider the extended Rapcsák system completed with the curvature condition. We prove that in the non-isotropic case there is a nontrivial Spencer cohomology group in the sequences determining the 2-acyclicity of the symbol of the corresponding differential operator. Therefore the system is not integrable and higher order obstruction exists.
LA - eng
KW - Euler-Lagrange equation; metrizability; projective metrizability; geodesics; spray; formal integrability
UR - http://eudml.org/doc/288197
ER -

References

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