Equivalence of Paths in Galilean Geometry

被引：0
作者：
Chilin V.I. [1 ]
Muminov K.K. [1 ]
机构：
[1] National University of Uzbekistan named after Mirzo Ulugbek, Tashkent
来源：
Journal of Mathematical Sciences | 2020年 / 245卷 / 3期
关键词：
53A15; 53A55; 53B30; differential invariant; Galilean space; path in a finitedimensional space; transcendence basis;
D O I：
10.1007/s10958-020-04691-7
中图分类号：
学科分类号：
摘要：
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. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.
引用
收藏
页码：297 / 310
页数：13
相关论文
共 27 条
  • [1] Aleksandrov P.S., A Course of Analytic Geometry and Linear Algebra [in Russian], (1979)
  • [2] Aminov Y.A., Differential Geometry and Topology [in Russia], (1987)
  • [3] Aripov R.G., Khadzhiev D., The complete system of global differential and integral invariants of a curve in Euclidean geometry, Izv. Vyssh. Uchebn. Zaved. Mat., 7, pp. 3-16, (2007)
  • [4] Blaschke W., Vorlesungen über Differentialgeometrie und geometrische Grundlagen von Einsteins Relativitätstheorie, (1921)
  • [5] Cartan E., La Théorie des Groupes Finis et Continus et la Géométrie Différentielle Traitées par la Méthode du Repère Mobile, (1937)
  • [6] Cartan E., Selected Papers [Russian translation], (1998)
  • [7] Chilin V.I., Muminov K.K., A complete system of differential invariants of curves in pseudo-Euclidean spaces, Dinam. Sist., 31, 3, pp. 135-149, (2013)
  • [8] Dieudonne J., Carrell J.B., Invariant Theory, (1971)
  • [9] Hilbert D., Selected Papers. Invariant Theory. Number Theory. Algebra. Geometry. Foundations of Mathematics [Russian translation], (1998)
  • [10] Kaplansky I., An Introduction to Differential Algebra, (1957)
123