Semiparallel wintgen ideal surfaces in En

Abstract

Wintgen ideal surfaces in E-4 form an important family of surfaces, namely surfaces with circular ellipse of curvature. Obviously, Wintgen ideal surfaces satisfy the pointwise equality K + vertical bar K-N vertical bar = parallel to H parallel to(2). In the present study we consider the Wintgen ideal surfaces in n-dimensional Euclidean space E-n. We have shown that Wintgen ideal surfaces in E-n satisfying the semiparallelity condition (R) over bar (X, Y) . h = 0 are of flat normal connection. Further, we obtain some results in E-4.