On Total Shear Curvature of Surfaces in E^{n+2}

Abstract

In the present study we consider surfaces in Euclidean (n+2)-space Eⁿ⁺². Firstly, we introduce some basic concepts of second fundamental form and curvatures of the surfaces in Eⁿ⁺². Further, we obtained some basic properties of surfaces in Eⁿ⁺² and some results related with their total shear curvatures. Finally, we give an example of generalized spherical surfaces in Euclidean 4-space E⁴ with vanishing shear curvature.