Rotational surfaces in isotropic spaces satisfying weingarten conditions

Abstract

Abstract:In this paper, we study the rotational surfaces in the isotropic 3-space I 3 satisfying Weingarten conditions in terms of the relative curvature K (analogue of the Gaussian curvature) and the isotropic mean curvature H. In particular, we classify such surfaces of linear Weingarten type in I 3 .

Linear Weingarten Helicoidal Surfaces in Isotropic Space

“…In the special case that M is a rotational surface (i.e., h = 0) in an isotropic three-dimensional space, we have the same result with Theorem 3.2 in Ögrenmiş's work as follows: Corollary 1. [18] Let M be a rotational surface in an isotropic three-dimensional space parameterized by X(u, v) = (u cos v, u sin v, g(u)).…”