Flat Rotational Surface with Pointwise 1-typeGauss map in E4
Ferda\u{g} Kahraman Aksoyak, Yusuf Yayl{\i}
TL;DR
This paper characterizes flat rotational surfaces in four-dimensional space with pointwise 1-type Gauss map and shows that non-planar examples are Clifford tori if they form Lie groups.
Contribution
It provides a new characterization of flat rotational surfaces with pointwise 1-type Gauss map in E4 and links non-planar cases to Clifford tori as Lie groups.
Findings
Flat general rotation surfaces with pointwise 1-type Gauss map are characterized.
Non-planar such surfaces are Clifford tori if they are Lie groups.
The paper establishes a link between geometric properties and Lie group structure.
Abstract
In this paper we study general rotational surfaces in the 4- dimensional Euclidean space E4 and give a characterization of flat general rotation surface with pointwise 1-type Gauss map. Also, we show that a non-planar flat general rotation surface with pointwise 1-type Gauss map is a Lie group if and only if it is a Clifford torus.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Mathematics and Applications · Geometric and Algebraic Topology