New Properties of Euclidean Killing Tensors of Rank Two

IF 0.5 Q4 PHYSICS, MATHEMATICAL

Journal of Geometry and Symmetry in Physics Pub Date : 2019-01-01 DOI:10.7546/jgsp-51-2019-1-7

M. Crasmareanu

引用次数: 1

Abstract

A symmetric tensor field on a Riemannian manifold is called a Killing tensor field if the symmetric part of its covariant derivative is equal to zero. There exists a well-known bijection between Killing tensor fields and conserved quantities of the geodesic flow which depend polynomially on the momentum variables. In particular, Killing tensors of rank (or valence) two yields quadratic first integrals and we discuss some aspects of this process in Crasmareanu [7] from a dynamical point of view. Some classes of physical examples associated with the Euclidean 2D metric are provided in Crasmareanu and Baleanu [8].

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二阶欧几里得杀伤张量的新性质

黎曼流形上的对称张量场如果其协变导数的对称部分等于零，则称为杀戮张量场。在消张量场和测地线流的守恒量之间存在一个众所周知的双射，它多项式地依赖于动量变量。特别地，二阶(价)消张量产生二次一积分，我们从动力学的角度讨论了这一过程的一些方面。在Crasmareanu和Baleanu[8]中提供了一些与欧几里得二维度量相关的物理例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Geometry and Symmetry in Physics PHYSICS, MATHEMATICAL-

CiteScore

1.50

自引率

25.00%

发文量

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