Spherical Product Surfaces in E4

Abstract

In the present study we calculate the coefficients of the second fundamental form and curvature ellipse of spherical product surfaces in E4. Otsuki rotational surfaces and Ganchev-Milousheva rotational surfaces are the special type of spherical product surfaces in E4. Further, we give necessary and sufficient condition for the origin of NpM to lie on the curvature ellipse of such surfaces. Finally we get the necessary condition for Ganchev-Milousheva rotational surfaces in E4 to become flat or Chen type. We also give some examples of the projections of these surfaces in E3

Keywords

• second fundamental form
• curvature ellipse
• spherical product
• otsuiki surface