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

Authors : Alev Kelleci Akbay

Pages : 137-143

Doi:10.33401/fujma.785781

View : 16 | Download : 11

Publication Date : 2020-12-15

Article Type : Research

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 condi tio n  $\Delta^{J}x_i=\lambda_i x_i,$   w ith  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