Semiparalel Wintgen Ideal Surfaces in E^n

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+K_N=H^2. In the present study we consider the Wintgen ideal surfaces in n-dimensional Euclidean space E^4. We have shown that Wintgen ideal surfaces in E^n satisfying the semiparallelity condition R(X,Y)h=0 are totally umbilical. Further, we obtain some results in E^4.

9 pages