About the integrability of the Rapcs\'ak equation
Tam\'as Milkovszki, Zolt\'an Muzsnay
TL;DR
This paper studies the integrability conditions of the Rapcsák equations related to Finsler geometry using advanced differential systems techniques, extending previous work on projective metrizability.
Contribution
It applies the Spencer version of the Cartan-Kähler theorem to analyze the integrability of the Rapcsák system and its extended version.
Findings
Established conditions for integrability of the Rapcsák system
Extended the analysis to include first integrability conditions
Provided a framework for future studies on Finsler metrizability
Abstract
In [17] A. Rapcs\'ak obtained necessary and sufficient conditions for the projective Finsler metrizability in terms of a second order partial differential equations. In this paper we investigate the integrability of the Rapcs\'ak system, consisting of the Rapcs\'ak equations and the homogeneity condition, by using the Spencer version of the Cartan-K\"ahler theorem. We also consider the extended Rapcs\'ak system, where the first integrability conditions are included.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Geometric Analysis and Curvature Flows · Fixed Point Theorems Analysis