On the solutions of weak normality equations in multidimensional case

doi:https://doi.org/10.48550/arxiv.math/0012110

Open AccessPreprint10.48550/arxiv.math/0012110

On the solutions of weak normality equations in multidimensional case

Руслан Шарипов-2000-12-14-ArXiv.org

TL;DRAbstract

The system of weak normality equations constitutes a part in the complete system of normality equations. Solutions of each of these two systems of equations are associated with some definite classes of Newtonian dynamical systems in Riemannian manifolds. In this paper for the case of simplest flat Riemannian manifold $M=\Bbb R^n$ with $n\geq 3$ we show that there exist solutions of weak normality equations that do not solve complete system of normality equations in whole. Hence associated classes of Newtonian dynamical systems do not coincide with each other.

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The system of weak normality equations constitutes a part in the complete system of normality equations. Solutions of each of these two systems of equations are associated with some definite classes of Newtonian dynamical systems in Riemannian manifolds. In this paper for the case of simplest flat Riemannian manifold $M=\Bbb R^n$ with $n\geq 3$ we show that there exist solutions of weak normality equations that do not solve complete system of normality equations in whole. Hence associated classes of Newtonian dynamical systems do not coincide with each other.

Keywords

NormalityMathematicsDynamical systems theoryRiemannian manifoldManifold (fluid mechanics)Simultaneous equationsSystem of linear equationsMathematical analysis

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