Generalized Rotation Surfaces in $${\mathbb E^4}$$

Abstract

In the present study we consider generalized rotation surfaces imbedded in an Euclidean space of four dimensions. We also give some special examples of these surfaces in E 4 . Further, the curvature properties of these surfaces are investigated. We give necessary and sufficient conditions for generalized rotation surfaces to become pseudo-umbilical. We also show that every general rotation surface is Chen surface in E 4 . Finally we give some examples of generalized rotation surfaces in E 4 .Mathematics Subject Classification (2010). Primary 53C40; Secondary 53C42.

A study on self-similar surfaces

“…Let we recall the coefficients of first and second fundamental form of a generalized rotation surface X(u, v) [5]:…”

Surface pencils in Euclidean 4-space 𝔼4

“…The surface given with the parametrization (1.1) is called pencil surface in E 4 . If γ(s) is a W-curve then M becomes a generalized rotation surface defined by Milousheva in [11] and see also [1,5].…”

The Gauss Map and the Third Laplace-Beltrami Operator of the Rotational Hypersurface in 4-Space

“…When we focus on the rotational characters in the literature, we meet Arslan et al [1,2], Arvanitoyeorgos et al [3], Chen [4,5], Dursun and Turgay [6], Kim and Turgay [7], Takahashi [8], and many others.…”

“…They classified completely the minimal rotational surfaces and those consisting of parabolic points. Arslan et al [2] studied generalized rotation surfaces in E 4 . Moreover, Dursun and Turgay [6] studied minimal and pseudo-umbilical rotational surfaces in E 4 .…”