Czechoslovak Mathematical Journal | |
On the projective Finsler metrizability and the integrability of Rapcsák equation | |
Tamás Milkovszki, Zoltán Muzsnay1  | |
关键词: Euler-Lagrange equation; metrizability; projective metrizability; geodesics; spray; formal integrability; | |
DOI : 10.21136/CMJ.2017.0010-16 | |
学科分类:数学(综合) | |
来源: Akademie Ved Ceske Republiky | |
【 摘 要 】
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.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO201910181395448ZK.pdf | 271KB | download |