Henneberg's algebraic surfaces in Minkowski 3-space

Year 2019, Volume: 68 Issue: 2, 1761 - 1773, 01.08.2019

Erhan Güler , Vahit Zambak

https://doi.org/10.31801/cfsuasmas.444554

Cited By: 2

Abstract

Bu çalışmada, üç boyutlu Minkowski uzayında Henneberg minimal yüzeyi ele alınmış olup yüzeyin derece, sınıf ve integralden bağımsız gösterinleri verilniştir.

Keywords

Weierstrass representation, spacelike maximal Henneberg surface, timelike minimal Henneberg surface, degree, class

References

• Fomenko A.T., Tuzhilin A.A., Elements of the Geometry and Topology of Minimal Surfaces in Three-Dimensional Space, Translated from the Russian by E.J.F. Primrose. Translations of Mathematical Monographs, 93. American Math. Soc., Providence, RI, 1991.
• Fujimori S., Saji K., Umehara M., Yamada K., Singularities of maximal surfaces, Math. Z. 259 (2008) 827--848.
• Gray A., Salamon S., Abbena E., Modern Differential Geometry of Curves and Surfaces with Mathematica, Third ed. Chapman & Hall/CRC Press, Boca Raton, 2006.
• Henneberg L., Über salche minimalfläche, welche eine vorgeschriebene ebene curve sur geodätishen line haben. Doctoral Dissertation, Eidgenössisches Polythechikum, Zürich, 1875.
• Henneberg L., Über diejenige minimalfläche, welche die Neil'sche Paralee zur ebenen geodätischen line hat, Vierteljschr Natuforsch, Ges. Zürich, 21 (1876) 66--70.
• Henneberg L., Bestimmung der neidrigsten Classenzahl der algebraischen Minimalflächen. Annali di Matem. Pura Appl. 9 (1878) 54--57.
• Inoguchi J., Lee S., Null curves in Minkowski 3-space, Int. Electron. J. Geom., 1, No. 2 (2008) 40--83.
• Kobayashi O., Maximal surfaces in the 3-dimensional Minkowski space L³, Tokyo J. Math. 6, No. 2 (1983) 297--309.
• Magid M., Timelike surfaces in Lorentz 3-space with prescribed mean curvature and Gauss map, Hokkaido Math. J. 20, No. 3 (1991) 447-464.
• Nitsche J.C.C., Lectures on Minimal Surfaces. Vol. 1. Introduction, Fundamentals, Geometry and Basic Boundary Value Problems, Cambridge Un. Press, Cambridge, 1989.
• Spivak M., A Comprehensive Introduction to Differential Geometry, Vol. IV. Third edition. Publish or Perish, Inc., Houston, Texas, 1999.
• Umehara M., Yamada K., Maximal surfaces with singularities in Minkowski space, Hokkaido Math. J. 35, 1 (2006) 13--40.
• Weierstrass K., Untersuchungen über die Flächen, deren mittlere Krümmung überall gleich Null ist, Monatsber. d. Berliner Akad. (1866) 612--625.
• Weierstrass K., Über die analytische Darstellbarkeit sogenannter willkürlicher Functionen einer reellen Veränderlichen, Sitzungsberichte der Akademie zu Berlin (An expanded version of this paper with ten additional pages appeared in Weierstrass, Mathematische Werke, Mayer and Müller, Berlin, Vol. 3, (1903), 1--37), (1885), 633--639 and 789--805.