Characterizations of Tzitzeica Curves Using Conformable Frenet Frame

Abstract

Tzitzeica curve is a mathematical curve that has been used to describe the behavior of certain physical phenomena. It was first discovered by Romanian mathematician Gheorghe Tzitzeica and has since been used to model many phenomena, including the motion of a pendulum, the oscillations of a vibrating string, and the flow of electricity through a circuit. The curve is an example of what is known as an elliptic curve and can be used to analyze complex systems. Its properties make it useful in many applications, such as cryptography and data compression. In the light of this information, the aim of this study, the conditions for a conformable curve and its spherical indicator curves to be a Tzitzeica curve will be examined. Thus, by understanding the behavior of the Tzitzeica curve, researchers can gain insight into complex systems and make more accurate predictions about their behavior. MSC Classification: 26A33 , 53A04 , 53A55