Ruled Weingarten Surfaces Related to Dual Spherical Curves

TL;DR

This paper investigates ruled surfaces in three-dimensional space derived from dual spherical indicatrix curves of dual Frenet vector fields, analyzing their curvature properties and conditions for being Weingarten surfaces.

Contribution

It introduces a method to construct ruled surfaces from dual spherical indicatrix curves and characterizes their Gaussian and mean curvatures, identifying conditions for Weingarten surfaces.

Findings

Derived formulas for Gaussian and mean curvatures of the ruled surfaces.

Identified conditions under which these surfaces are Weingarten surfaces.

Provided geometric insights into the properties of ruled surfaces related to dual spherical curves.

Abstract

We study ruled surfaces in R3 which are obtained from dual spher- ical indicatrix curves of dual Frenet vector fields. We find the Gaussian and mean curvatures of the ruled surfaces and give some results of being Wein- garten surface.