The Fermi–Walker Derivative on the Spherical Indicatrix of Timelike Curve in Minkowski 3-Space

In this paper Fermi–Walker derivative and Fermi–Walker parallelism and non-rotating frame concepts are given along the spherical indicatrix of a timelike curve in E13\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${E_{1}^{3}}$$\end{document}. First, we consider a timelike curve in the Minkowski space and investigate the Fermi–Walker derivative along the tangent. The concepts which Fermi–Walker derivative are analyzed along its tangent. Then, the Fermi–Walker derivative and its theorems are analyzed along the principal normal indicatrix and the binormal indicatrix of timelike curve in E13\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${E_{1}^{3}}$$\end{document}.