On the solutions of weak normality equations in multidimensional case

Abstract

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 $M={\mathbb{R}}^n$ with $n\ge 3$ 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.

AmSTeX, 16 pages, amsppt style

References in corpus (6)

• Dynamical Systems Accepting the Normal Shift
• Problem of Metrizability for the Dynamical Systems Accepting the Normal Shift
• Dynamical systems accepting the normal shift on an arbitrary Riemannian manifold
• Two-dimensional dynamical systems admitting the normal shift
• Newtonian dynamical systems admitting normal blow-up of points
• Complete normality conditions for the dynamical systems on Riemannian manifolds

Cited by in corpus (5)

• Normal shift in general Lagrangian dynamics
• On the concept of normal shift in non-metric geometry
• Comparative analysis for pair of dynamical systems, one of which is Lagrangian
• V-representation for normality equations in geometry of generalized Legendre transformation
• On the subset of normality equations describing generalized Legendre transformation