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

Year 2020, Volume: 3 Issue: 2, 137 - 143, 15.12.2020

Alev Kelleci Akbay

https://doi.org/10.33401/fujma.785781

Abstract

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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