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

Author

Listed:
  • 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)

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 ) .

Suggested Citation

  • Erhan Güler & Ömer Kişi & Christos Konaxis, 2018. "Implicit Equations of the Henneberg-Type Minimal Surface in the Four-Dimensional Euclidean Space," Mathematics, MDPI, vol. 6(12), pages 1-10, November.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:12:p:279-:d:185353
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