Tubular Involutive Surfaces with Frenet Frame in Euclidean 3-Space

Abstract

In this study we first define the tubular involutive surfaces as a new surface form. We then investigate singularity, Gaussian curvature and mean curvatures of the tubular involutive surfaces and get an interesting relation between these curvatures as 2H = -(rK + 1/r). By calculating the Gaussian and mean curvatures of the tubular involutive surfaces, we find the necessary conditions of being flat or minimal of these surfaces. In addition, we analyse the necessary and sufficient conditions for parameter curves on the surface to be asymptotic, geodesic and line of curvature. Finally, we illustrate our method by presenting two examples.