On the projective Finsler metrizability and the integrability of Rapcsák equation

Title:

On the projective Finsler metrizability and the integrability of Rapcsák equation

Creator:

Milkovszki, Tamás and Muzsnay, Zoltán

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:8c9d4bea-a635-4985-88d5-afd57ab8157b
uuid:8c9d4bea-a635-4985-88d5-afd57ab8157b
issn:0011-4642

Subject:

matematika, mathematics, formal integrability, spray, geodesics, Euler-Lagrange equation, metrizability, projective metrizability, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

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., Tamás Milkovszki, Zoltán Muzsnay., and Seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

469-495

Source:

Czechoslovak Mathematical Journal | 2017 Volume:67 | Number:2

Harvested from:

CDK

Metadata only:

false