Simultaneous characterizations of partner ruled surfaces using Flc frame

Abstract

<abstract><p>In this study, we introduce partner ruled surfaces according to the Flc frame that is defined on a polynomial curve. First, the conditions of each couple of two partner ruled surfaces to be simultaneously developable and minimal are investigated. Then, the asymptotic, geodesic and curvature lines of the parameter curves of the partner ruled surfaces are simultaneously characterized. Finally, the examples of the partner ruled surfaces are given, and their graphs are drawn.</p></abstract>

A Study of Conformal $$\eta$$-Einstein Solitons on Trans-Sasakian 3-Manifold

“…Finally combining Eqs. ( 37) and (38), we arrive at Thus the above discussion leads to the following:…”

“…Then = − p 2 + 7 3 . The value of and satisfies the relation (38) and (39). So, g defines a conformal -Einstein solitons on trans-Sasakian 3-manifold for = − p 2 + 7 3 and = 6 .…”

“…( 35) holds and combining (35) with the above Eq. (76), we get Again recalling the equation (38) in the above (77), we achieve…”

On Ruled Surfaces Constructed by the Evolution of a Polynomial Space Curve

“…T X be a tangent ruled surface with the Flc frame, then the surface (11) where the curvatures 1 d and 3 d depend on the parameters s and t . By considering the partial derivatives of the surface 2 D X given by Eq (10) and Eq.…”

“…To solve this problem, Dede defined the Flc frame for moving polynomial curves [7,8]. The Flc frame [9][10][11][12][13] and ruled surfaces on different frames [14][15][16][17][18][19][20][21][22][23] have been investigated by many researchers. Inspired by these studies, we conducted this research to create a new resource on the subject of surfaces and to form a basis for future studies.…”