Classifications of THA-surfaces in I^3

Abstract

In classical differential geometry, the problem of obtaining Gaussian and mean curvatures of a surface is one of the most important problems. A surface M² in I³ is a THA-surface of first type if it can be parameterized by r(s, t) = (s, t, Af(s + at)g(t) + B(f(s + at) + g(t))). A surface M² in I³ is a THA- surface of second type if it can be parameterized by r(s, t) = (s, Af(s + at)g(t) + B(f(s + at) + g(t)), t), where A and B are non-zero real numbers [16, 17, 18]. In this paper, we classify two types THA-surfaces in the 3-dimensional isotropic space I³ and study THA-surfaces with zero curvature in I³.