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arxiv: 1305.2336 · v1 · pith:Q65YLU4Dnew · submitted 2013-05-10 · 🧮 math.DG

Semiparalel Wintgen Ideal Surfaces in E^n

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keywords surfacesidealwintgencircularconditionconsidercurvatureellipse
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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.

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