Semi-parallel and harmonic surfaces in semi-Euclidean 4-space with index two

Abstract

The present paper mainly deals with construction and investigation further properties of semi-parallel and harmonic surfaces. The first part of the study shall be devoted to investigate and present necessary and sufficient conditions of being semi-parallel surfaces by considering semi-parallelity condition $R(X,Y).h=0$. In the light of these conditions, the fact of a part of semi-parallel surfaces can be created by translation surfaces is captured. As a last result, we present that $M $ must be a translation surface in the case of it is a harmonic surface.