Classification of Some Special Types Ruled Surfaces in Simply Isotropic 3-Space

Abstract

Abstract. In this paper, we classify two types ruled surfaces in the three dimensional simply isotropic space I 1 3 under the condition ∆x i = λ i x i where ∆ is the Laplace operator with respect to the first fundamental form and λ is a real number. We also give explicit forms of these surfaces.

Warped Translation Surfaces of Finite Type in Simply Isotropic 3-Spaces

“…where J = I, II and i = 1, 2, 3, in these spaces in [20,21] and [22], respectively. Also, in [23], [24] and [25], authors studied affine translation surfaces, helicoidal surfaces and ruled surfaces satisfying the same condition.…”