EQUIVALENCE OF PATHS IN GALILEAN GEOMETRY

In this paper, we present an explicit description of finite transcendence bases in the differential field of differential rational functions that are invariant under the action of the Galilean transformation group in a real finite-dimensional space. Necessary and sufficient conditions of the equivalence of paths in the n-dimensional Galilean space are obtained. Keywords and phrases: Galilean space, differential invariant, transcendence basis, path in a finite dimensional space. AMS Subject Classification: 53A15, 53A55, 53B30
UDC 512.74 CONTENTS 1. Introduction 2. Preliminaries 3. Transcendence Basis in the Differential Field of Differential Rational Functions That Are Invariant under the Action of the Galilean Group 4. Equivalence [...]