Parabolic Revolution Surfaces of Finite Type in Simply Isotropic 3-spaces

In this paper, we classify parabolic revolution surfaces in the three-dimensional simply isotropic space [Formula: see text] under the condition [Formula: see text] where [Formula: see text] is the Laplace operator with respect to first and second fundamental form and [Formula: see text], [Formula: see text] are some real numbers. Also, as an application, we give some explicit examples for these surfaces.

Translation surfaces in the three-dimensional simply isotropic space 𝕀31

In [M. K. Karacan, D. W. Yoon and B. Bukcu, Translation surfaces in the three-dimensional simply isotropic space [Formula: see text], Int. J. Geom. Methods Mod. Phys. 13(7) (2016) 1650088], there is a mistake in Theorem 5 that appeared in the paper. We here provide a correct theorem.

Dual translation surfaces in the three dimensional simply isotropic space $\mathbb{I}_{3}^{1}$

In this paper, we study the dual translation surfaces in three dimensional simply isotropic space. We give classification of dual translation surface with constant dual isotropic mean curvature or constant dual isotropic Guassian curvature.

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

In this paper, we classify two types ruled surfaces in the three dimensional simply isotropic space I13under the condition ∆xi= λixiwhere ∆ 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.

Helicoidal Surfaces in the three dimensional simply isotropic space I₃¹

In this paper, we classify helicoidal surfaces in the three dimensional simply isotropic space I₃¹ satisfying some algebraic equations in terms of the coordinate functions and the Laplacian operators with respect to the first, the second and the third fundamental form of the surface. We also give explicit forms of these surfaces.