Weingarten Map of the Henneberg-Type Minimal Surfaces in 4-Space

Year 2021, Volume: 9 Issue: 1, 132 - 136, 28.04.2021

Erhan Güler , Ömer Kişi

Abstract

We consider a two parameter family of Henneberg-type minimal surfaces $ \mathfrak{H}_{m,n}$ using the Weierstrass representation in the four dimensional Euclidean space $\mathbb{E}^{4}$. An invariant linear map of Weingarten type in the tangent space of the Henneberg-type minimal surface $\mathfrak{H}_{4,2}$ which generates two invariants $\kappa $ and $\varkappa $, is characterized by $ \varkappa^{2}=\kappa $ in $\mathbb{E}^{4}$.

Keywords

Four dimension, Henneberg-type minimal surface, Weierstrass representation, Weingarten map

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