The Transformation of the Evolute Curves Using Lifts on R^3 to Tangent Space Tr^3
HAŞİM ÇAYIR,
SÜLEYMAN ŞENYURT
Abstract:In this paper, firstly, we define the evolute curve of any curve concerning the vertical, complete, and horizontal lifts on space R^3 to its tangent space TR^3=R^6. Secondly, we examine the Frenet-Serret apparatus {T^* (s),N^* (s),B^* (s),κ^*,τ^* } and the Darboux vector W^* of the evolute curve α^* according to the vertical, complete and horizontal lifts on TR^3 by depend on the lifting of Frenet-Serret aparatus {T(s),N(s),B(s),κ,τ} of the first curve α on space R^3. In addition, we include all special cases … Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.