TY - JOUR
TI - Harmonicity and differential equation of involute of a curve in E3
AU - Çakir Osman
AU - Şenyurt Süleyman
JN - Thermal Science
PY - 2019
VL - 23
IS - 16
SP - 2119
EP - 2125
PT - Article
AB - In this paper, we first give necessary conditions in which we can decide  whether a given curve is biharmonic or 1-type harmonic and differential  equations characterizing the regular curves. Then we research the Frenet  formulas of involute of a unit speed curve by making use of the relations  between the involute of a curve and the curve itself. In addition we apply  these formulas to define the essential conditions by which one can determine  whether the involute of a unit speed curve is biharmonic or 1-type harmonic  and then we write differential equations characterizing the involute curve  by means of Frenet apparatus of the unit speed curve. Finally we examined  the helix as an example to illustrate how the given theorems work.