Fermi-Walker Parallel Transport According to Quasi Frame in Three Dimensional Minkowski Space

IF 0.5 Q4 PHYSICS, MATHEMATICAL

Journal of Geometry and Symmetry in Physics Pub Date : 2019-01-01 DOI:10.7546/jgsp-54-2019-1-12

N. Gürbüz, D. Yoon

引用次数: 0

Abstract

A relativistic observer ξ needs reference frames in order to measure the movement and position of a object. If ξ is free falling, its restspaces are transported with LeviCivita parallelism. For accelerated observes, the restspaces are not transported by the Levi-Civita parallelism. In this case Fermi-Walker parallelism is used to define constant directions. Fermi-Walker parallelism is an isometry between the tangent spaces along relativistic observer ξ. [6, 11]. Balakrishnan et al investigated time evolutions of the space curve associated with a geometric phase using Fermi-Walker parallel transport in three dimensional Euclidean space [2]. Gürbüz had introduced new geometric phases according three classes of a curve evolution in Minkowski space [7, 8]. Usual Fermi-Walker parallel derivative for any vector field A is given with respect to Frenet frame {t, n, b} in three dimensional Euclidean space as following (cf. [9]) DfA Dfs = dA

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三维闵可夫斯基空间中准坐标系下的费米-沃克平行输运

一个相对论观察者ξ需要参考系来测量一个物体的运动和位置。如果ξ是自由落体的，则其剩余空间以列维维塔平行度传输。对于加速观测，静止空间不受列维-奇维塔平行度的传输。在这种情况下，费米-沃克平行度被用来定义恒定方向。费米-沃克平行度是沿相对论观察者ξ的切空间之间的等距。(6, 11)。Balakrishnan等人利用三维欧几里得空间[2]中的费米-沃克平行输运研究了与几何相位相关的空间曲线的时间演化。g rb z根据Minkowski空间中曲线演化的三类引入了新的几何相[7,8]。通常在三维欧几里德空间中，任意向量场A对Frenet坐标系{t, n, b}的费米-沃克平行导数如下(cf. [9]) DfA Dfs = dA

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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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