On Generalized Spherical Surfaces in Euclidean Spaces

2016/05/02 by Bengü Bayram, Bayram, Bengu, Kadri Arslan +3
Mathematics · Physics and Astronomy · #53C40 #53C42 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1605.00460

openalex publication_date 2016/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 𝔼ⁿ⁺¹. Further, we introduce some kind of generalized spherical surfaces in Euclidean spaces 𝔼³ and % 𝔼⁴ respectively. We have shown that the generalized spherical surfaces of first kind in 𝔼⁴ are known as rotational surfaces, and the second kind generalized spherical surfaces are known as meridian surfaces in 𝔼⁴. We have also calculated the Gaussian, normal and mean curvatures of these kind of surfaces. Finally, we give some examples.

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