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Henneberg's algebraic surfaces in Minkowski 3-space

Yıl 2019, Cilt: 68 Sayı: 2, 1761 - 1773, 01.08.2019
https://doi.org/10.31801/cfsuasmas.444554

Öz

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

Kaynakça

  • 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.
Yıl 2019, Cilt: 68 Sayı: 2, 1761 - 1773, 01.08.2019
https://doi.org/10.31801/cfsuasmas.444554

Öz

Kaynakça

  • 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.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Erhan Güler 0000-0003-3264-6239

Vahit Zambak Bu kişi benim 0000-0003-3264-6239

Yayımlanma Tarihi 1 Ağustos 2019
Gönderilme Tarihi 17 Temmuz 2018
Kabul Tarihi 6 Mart 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 68 Sayı: 2

Kaynak Göster

APA Güler, E., & Zambak, V. (2019). Henneberg’s algebraic surfaces in Minkowski 3-space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1761-1773. https://doi.org/10.31801/cfsuasmas.444554
AMA Güler E, Zambak V. Henneberg’s algebraic surfaces in Minkowski 3-space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Ağustos 2019;68(2):1761-1773. doi:10.31801/cfsuasmas.444554
Chicago Güler, Erhan, ve Vahit Zambak. “Henneberg’s Algebraic Surfaces in Minkowski 3-Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, sy. 2 (Ağustos 2019): 1761-73. https://doi.org/10.31801/cfsuasmas.444554.
EndNote Güler E, Zambak V (01 Ağustos 2019) Henneberg’s algebraic surfaces in Minkowski 3-space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1761–1773.
IEEE E. Güler ve V. Zambak, “Henneberg’s algebraic surfaces in Minkowski 3-space”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 68, sy. 2, ss. 1761–1773, 2019, doi: 10.31801/cfsuasmas.444554.
ISNAD Güler, Erhan - Zambak, Vahit. “Henneberg’s Algebraic Surfaces in Minkowski 3-Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (Ağustos 2019), 1761-1773. https://doi.org/10.31801/cfsuasmas.444554.
JAMA Güler E, Zambak V. Henneberg’s algebraic surfaces in Minkowski 3-space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1761–1773.
MLA Güler, Erhan ve Vahit Zambak. “Henneberg’s Algebraic Surfaces in Minkowski 3-Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 68, sy. 2, 2019, ss. 1761-73, doi:10.31801/cfsuasmas.444554.
Vancouver Güler E, Zambak V. Henneberg’s algebraic surfaces in Minkowski 3-space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1761-73.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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