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

Erhan Güler, Ömer Kişi and Christos Konaxis
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Erhan Güler: Department of Mathematics, Faculty of Sciences, Bartın University, 74100 Bartın, Turkey
Ömer Kişi: Department of Mathematics, Faculty of Sciences, Bartın University, 74100 Bartın, Turkey
Christos Konaxis: Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, 15784 Athens, Greece

Mathematics, 2018, vol. 6, issue 12, 1-10

Abstract: 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 ) .

Keywords: Henneberg-type minimal surface; Weierstrass representation; four-dimensional space; implicit equation; degree (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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