Semiparalel Wintgen Ideal Surfaces in E^n

TL;DR

This paper investigates Wintgen ideal surfaces in higher-dimensional Euclidean spaces, establishing conditions under which these surfaces are totally umbilical, and provides specific results in four-dimensional space.

Contribution

It extends the study of Wintgen ideal surfaces to E^n and characterizes those satisfying the semiparallelity condition as totally umbilical surfaces.

Findings

Wintgen ideal surfaces in E^n with R(X,Y)h=0 are totally umbilical.

Specific results are obtained for Wintgen ideal surfaces in E^4.

The study enhances understanding of curvature conditions for these surfaces.

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.