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TRANSLATION AND HOMOTHETICAL SURFACES IN EUCLIDEAN SPACE WITH CONSTANT CURVATURE

Rafael L\'opez|Marilena Moruz
대한수학회 (The Korean Mathematical Society)|2015.05|대한수학회지 (Journal of the KMS)|제52권 제3호|pp. 523-535

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참고문헌

키워드

Gauss curvaturemean curvaturetranslation surfacehomothetical surface
주제분류수학

초록

We study surfaces in Euclidean space which are obtained as the sum of two curves or that are graphs of the product of two functions. We consider the problem of finding all these surfaces with constant Gauss curvature. We extend the results to non-degenerate surfaces in Lorentz- Minkowski space.

Abstract

We study surfaces in Euclidean space which are obtained as the sum of two curves or that are graphs of the product of two functions. We consider the problem of finding all these surfaces with constant Gauss curvature. We extend the results to non-degenerate surfaces in Lorentz- Minkowski space.

참고문헌 (10)

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  2. J. G. Darboux, "Th´eorie G´enerale des Surfaces, Livre I" (1914), Gauthier-Villars
  3. F. Dillen, "The surface of Scherk in E3 : a special case in the class of minimal surfaces defined as the sum of two curves", Bull. Inst. Math. Acad. Sin, 26(4), pp.257~267 (1998)
  4. L. Jiu, "On minimal homothetical hypersurfaces", Colloq. Math, 109(2), pp.239~249 (2007)
  5. H. Liu, "Translation surfaces with constant mean curvature in 3-dimensional spaces", J. Geom, 64(1-2), pp.141~149 (1999)
  6. R. L´opez, "Differential Geometry of curves and surfaces in Lorentz-Minkowski space", Int. Electron. J. Geom, 7(1), pp.44~107 (2014)
  7. J. C. C. Nitsche, "Lectures on Minimal Surfaces. Vol. 1" (1989), Cambridge University Press
  8. H. F. Scherk, "Bemerkungen ¨uber die kleinste Fl¨ache innerhalb gegebener Grenzen", J. Reine Angew. Math, 13, pp.185~208 (1835)
  9. I. Van de Woestyne, "A new characterization of the helicoids, Geometry and topology of submanifolds, V", pp.267~273 (1993), World Sci. Publ
  10. I. Van de Woestyne, "Minimal homothetical hypersurfaces of a semi-Euclidean space", Results Math, 27(3-4), pp.333~342 (1995)

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