Tubular W-Surfaces in 3-Space (Report‪)‬

[section]1. Introduction and preliminaries Classically, a Weingarten surface or linear Weingarten surface (or briefly, a W-surface) is a surface on which there is a nontrivial functional relation [PHI] ([k.sub.1], [k.sub.2]) = 0 between its principal curvatures [k.sub.1] and [k.sub.2] or equivalently, there is a nontrivial functional relation [PHI] (K, H) = 0 between its Gaussian curvature K and mean curvature H. The existence of a nontrivial functional relation [PHI](A, B) = 0 such that [PHI] is of class [C.sup.1] is equivalent to the vanishing of the corresponding Jacobian determinant, namely, [partial derivative](A,B)/[partial derivative](s,t) = 0, where (A, B) = ([k.sub.1], [k.sub.2]) or (K, H) [4,5].