Article
Kyungpook Mathematical Journal 2022; 62(3): 509-531
Published online September 30, 2022
Copyright © Kyungpook Mathematical Journal.
On Ruled Surfaces with a Sannia Frame in Euclidean 3-space
S{ü}leyman Şenyurt∗, Kemal Eren
Department of Mathematics, Ordu University, Ordu, Turkey
e-mail : senyurtsuleyman52@gmail.com
Department of Mathematics, Sakarya University, Sakarya, Turkey
e-mail : kemal.eren1@ogr.sakarya.edu.tr
Received: November 25, 2021; Revised: February 14, 2022; Accepted: February 22, 2022
In this paper we define a new family of ruled surfaces using an othonormal Sannia frame defined on a base consisting of the striction curve of the tangent, the principal normal, the binormal and the Darboux ruled surface. We examine characterizations of these surfaces by first and second fundamental forms, and mean and Gaussian curvatures. Based on these characterizations, we provide conditions under which these ruled surfaces are developable and minimal. Finally, we present some examples and pictures of each of the corresponding ruled surfaces.
Keywords: Ruled surfaces, Sannia frame, striction curve, mean curvature, Gaussian curvature