On Generalized Spherical Surfaces in Euclidean Spaces

Abstract

In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized spherical curves in Euclidean $(n+1)-$space ${\mathbb{E}}^{n+1}$. Further, we introduce some kind of generalized spherical surfaces in Euclidean spaces ${\mathbb{E}}^3$ and respectively. We have shown that the generalized spherical surfaces of first kind in ${\mathbb{E}}^4$ are known as rotational surfaces, and the second kind generalized spherical surfaces are known as meridian surfaces in ${\mathbb{E}}^4$. We have also calculated the Gaussian, normal and mean curvatures of these kind of surfaces. Finally, we give some examples.

14 pages. arXiv admin note: text overlap with arXiv:1205.2143 by other authors