Surfaces at a constant distance from the edge of regression on a surface

On the tubular surfaces in E3

“…First of all, Tarakcı and Hacısalihoglu are the first ones to introduce surfaces at a constant distance from the edge of regression on a surface in E 3 in 2002 [1]. Actually, these surfaces were based on the study which is curve at a constant distance from the edge of regression on a curve proposed by Hans Vogler in 1963.…”

“…Actually, these surfaces were based on the study which is curve at a constant distance from the edge of regression on a curve proposed by Hans Vogler in 1963. They obtained surfaces at a constant distance from the edge of regression on a surface in E 3 taking a surface instead of a curve and calculated for these surfaces some properties and theorems known for parallel surfaces [2]. Later, conjugate tangent vectors and asymptotic directions for these surfaces are given in [3].…”

“…In 2014, Yurttançikmaz and Tarakcı investigated the relationship between focal surfaces and surfaces at a constant distance from the edge of regression on a surface [8]. Surface at a constant distance from the edge of regression on a surface of revolution in E 3 [9] and the image curves on surfaces at a constant distance from the edge of regression on a surface of revolution are given in [10] In relation to the concept of curvature, in recent times some authors studied Riemannian metric g and curvature tensor field R of Riemannian manfolds on tangent bundle [11,12,13].…”

“…Here, φ uu ,φ uv , φ vu , N u , N v are calculated as like as [1]. If parameter curves are line of curvatures of M and let u and v be arc lenght of these line of curvatures, we have following equations.…”

The Relationship between Focal Surfaces and Surfaces at a Constant Distance from the Edge of Regression on a Surface

“…Surfaces at a constant distance from the edge of regression on a surface were firstly defined by Tarakci in 2002 [1]. These surfaces were obtained by taking a surface instead of a curve in the study suggested by Hans Vogler in 1963.…”