Parabolic revolution surfaces of finite type in simply isotropic 3-spaces

Abstract

In this paper, we classify parabolic revolution surfaces in the three-dimensional simply isotropic space II3 under the condition Delta(J)x(i) = lambda(i)x(i), J = I, II, where 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 explicit examples for these surfaces.