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Bonnet–Thomsen surfaces in Minkowski geometry

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Abstract

We classify the analogues to the Bonnet–Thomsen surfaces in Minkowski geometry.

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References

  1. Alias L.J., Chaves R.M.B., Mira P.: Björling problem for maximal surfaces in Lorentz–Minkowski space. Math. Proc. Camb. Philos. Soc. 134, 289–316 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Blaschke W.: Vorlesungen über Differentialgeometrie, Band II: Affine Differentialgeometrie. Springer, Berlin (1923)

    Google Scholar 

  3. Böhm W.: Die Konstruktion der Minimalfläche von Enneper. Arch. Math. 12, 238–240 (1961)

    Article  MATH  MathSciNet  Google Scholar 

  4. Brauner H.: Eine Kennzeichnung der Minimalflächen von G.Thomsen. Rad Jugoslav. Akad. Znan. Umjet. 435, 1–15 (1988)

    MathSciNet  Google Scholar 

  5. Glässner E.: Über die Minimalflächen der zweiten Fundamentalform. Monatsh. Math. 78, 193–214 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  6. Gu C.H.: The extremal surfaces in the 3-dimansional Minkowski space. Acta Math. Sin. New Ser. 1, 173–180 (1985)

    Article  MATH  Google Scholar 

  7. Kobayashi O.: Maximal surfaces in the 3-dimensional Minkowski space L 3. Tokyo J. Math. 6, 297–309 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kühnel, W.: Differentialgeometrie 5. Auflage, Vieweg, Braunschweig (2010)

  9. Manhart, F.: Minkowski Minimal Surfaces in \({\mathbb{R}^3_1}\) with Minimal Focal Surfaces. Beitr. Algebra Geom. 50(2), 449–468 (2009)

  10. McNertney, L.: One-parameter families of surfaces with constant curvature in Lorentz 3-space. Ph.D. thesis Brown University (1980) (unpublished)

  11. Mira P., Pastor J.A.: Helicoidal maximal surfaces in Lorentz–Minkowski space. Monatsh. Math. 140, 315–334 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  12. Nitsche J.C.C.: Vorlesungen über Minimalflächen. Springer, Berlin (1975)

    Book  MATH  Google Scholar 

  13. Nomizu K., Sasaki T.: Affine Differential Geometry. Cambridge University Press, Cambridge (1994)

    MATH  Google Scholar 

  14. Pabel. H.: Deformationen von Minimalflächen. In: Geometrie und ihre Anwendungen. Hrsg. O.Giering und J.Hoschek. Carl Hanser, München-Wien (1994)

  15. Schaal H.: Die Affinminimalflächen von G. Thomsen. Arch. Math. 24, 208–217 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  16. Schaal H.: Neue Erzeugungen der Minimalflächen von G. Thomsen. Monatsh. Math. 77, 433–461 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  17. Schaal H.: Die Ennepersche Minimalfläche als Grenzfall der Minimalfläche von G. Thomsen. Arch. Math. 24, 320–322 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  18. Strubecker K.: Eine neue Erzeugung der Minimalfläche von Enneper. Annali di Matematica Pura ed Applicata 55(1), 297–305 (1961)

    Article  MathSciNet  Google Scholar 

  19. Thomsen G.: Über affine Geometrie XXXIX. Über Affinminimalflächen, die gleichzeitig Minimalflächen sind. Abh. Math. Sem. Hamburg 2, 71–73 (1923)

    Article  MATH  MathSciNet  Google Scholar 

  20. Weinstein, T.: An Introduction to Lorentz Surfaces. De Gruyter Expositions in Mathematics, vol. 22. de Gruyter, Berlin (1996)

  21. van de Woestijne, I.: Minimal Surfaces in 3-dimensional Minkowski space. In: Boyom, M. et al., (eds.) Geometry and Topology of Submanifolds II, pp. 344–369. World scientific, Singapore (1990)

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Authors and Affiliations

  1. Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstraße 8-10/1043, 1040, Wien, Austria

    Friedrich Manhart

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  1. Friedrich Manhart
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Correspondence to Friedrich Manhart.

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To Otto Röschel on the occasion of his 60th birthday

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Manhart, F. Bonnet–Thomsen surfaces in Minkowski geometry. J. Geom. 106, 47–61 (2015). https://doi.org/10.1007/s00022-014-0231-5

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  • DOI: https://doi.org/10.1007/s00022-014-0231-5

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