On the projective Finsler metrizability and the integrability of Rapcsák equation
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-Kä...
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| Veröffentlicht in: | Czechoslovak Mathematical Journal 2017-06, Vol.67 (2), p.469-495 |
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| creator | Milkovszki, Tamás Muzsnay, Zoltán |
| description | 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. |
| doi_str_mv | 10.21136/CMJ.2017.0010-16 |
| format | Article |
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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. 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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. 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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.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.21136/CMJ.2017.0010-16</doi><tpages>27</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Analysis Convex and Discrete Geometry Curvature Integral calculus Integral equations Mathematical analysis Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Ordinary Differential Equations |
| title | On the projective Finsler metrizability and the integrability of Rapcsák equation |
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