Some Characterizations of Tubular Surfaces and their Focal Surfaces in Euclidean 3-Space

Abstract

In this study, we examine the focal surfaces of tubular surfaces in Euclidean 3 space. We achieve some significant results for these surfaces in accordance with the modified orthogonal frame. Additionally, we propose a few geometric invariants that illustrate the geometric characteristics of these surfaces, such as flat, minimal, Weingarten, and linear-Weingarten surfaces, using the traditional methods of differential geometry. Additionally, these surfaces’ asymptotic and geodesic curves have been researched. At the last, we present an example as an instance of use to validate our theoretical findings. MSC(2010). 53A05, 53B25.