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

In this paper, we classify warped translation surfaces being invariant surfaces of i-type, that is, the generating curve has formed by the intersection of the surface with the isotropic xz-plane in the three-dimensional simply isotropic space $\mathbb I^3$ under the condition $\Delta^{J}x_i=\lambda_i x_i,$ with J=I,II. Here, $\Delta^{J}$ is the Laplace operator with respect to first and second fundamental form and $\lambda_i$, $i=1,2,3$ are some real numbers. Also, as an application, we give some examples for these surfaces and also some explicit graphics of them. All graphics have been plotted with Maple14.

Keywords:

Invariant surface, Laplace operator, Simply isotropic space Surfaces of finite type,

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