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Open AccessArticle

Implicit Equations of the Henneberg-Type Minimal Surface in the Four-Dimensional Euclidean Space

1
Department of Mathematics, Faculty of Sciences, Bartın University, 74100 Bartın, Turkey
2
Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, 15784 Athens, Greece
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(12), 279; https://doi.org/10.3390/math6120279
Received: 18 October 2018 / Revised: 20 November 2018 / Accepted: 22 November 2018 / Published: 25 November 2018
(This article belongs to the Special Issue Computer Algebra in Scientific Computing)
Considering the Weierstrass data as ( ψ , f , g ) = ( 2 , 1 - z - m , z n ) , we introduce a two-parameter family of Henneberg-type minimal surface that we call H m , n for positive integers ( m , n ) by using the Weierstrass representation in the four-dimensional Euclidean space E 4 . We define H m , n in ( r , θ ) coordinates for positive integers ( m , n ) with m 1 , n - 1 , - m + n - 1 , and also in ( u , v ) coordinates, and then we obtain implicit algebraic equations of the Henneberg-type minimal surface of values ( 4 , 2 ) . View Full-Text
Keywords: Henneberg-type minimal surface; Weierstrass representation; four-dimensional space; implicit equation; degree Henneberg-type minimal surface; Weierstrass representation; four-dimensional space; implicit equation; degree
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Güler, E.; Kişi, Ö.; Konaxis, C. Implicit Equations of the Henneberg-Type Minimal Surface in the Four-Dimensional Euclidean Space. Mathematics 2018, 6, 279.

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