Open AccessParallel Transport Frame of Smarandache Curves in Euclidean Space
Author(s) -
Shankar Lal
Publication year - 2021
Publication title -
journal of mountain research/journal of mountain research
Language(s) - English
Resource type - Journals
eISSN - 2582-5011
pISSN - 0974-3030
DOI - 10.51220/jmr.v16i1.23
Subject(s) - frenet–serret formulas , section (typography) , euclidean space , euclidean geometry , mathematics , parallel transport , frame (networking) , moving frame , space (punctuation) , geometry , differential geometry , mathematical analysis , space frame , curvature , computer science , physics , telecommunications , operating system , thermodynamics
In the present work, we introduce Parallel transport frames of Smarandache curves in Euclidean space. In the first section, we give the basic tools of a parallel transport frame of a curve in 4-dimensional Euclidean space. In the second section, we study Smarandache curve of Euclidean space in parallel transport frame, we solve a few theorems, corollaries and examples. Again third section, we define parallel transport frame to the Smarandachecurve and obtain some definitions and their apparatus. Further fourth section, we have also explained to Frenet frame of principal normal, binomial and their derivatives in the curvatures of the curve. In the end section, we discussed about the Smarandache curve in the Euclidean space of all apparatus Frenet-Serret in the differential geometry.