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Translation Surfaces With Constant Mean Curvature or Gauss Curvature in 3-Dimensional Spaces

Razgordani Sharahi, Masumeh | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 45055 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Fanaii, Hamid Reza
  7. Abstract:
  8. In Euclidean space R3 , a surface is called a translation surface if it is given by an immersion X : U 2 Rn ! Rn+1 : (x1; :::; xn) ! (x1; :::; xn; f1(x1) + ::: + fn(xn)) where fi; i = 1; ::; n are smooth functions.In this work, we give the classification of translation surfaces with constant mean curvature or Gauss curvature in 3-dimentional Euclidean space R3 and 3-dimentional Minkowski space L3 and We also characterize the minimal surfaces in the upper half-space model of 3-dimentional hyperbolic space H3 and we express this contents for spaces with arbitrary dimentional too
  9. Keywords:
  10. Minkowski Space ; Hyperbolic Space ; Minimal Surfaces ; Translation Surfaces ; Mean Curvature ; Gauss Curvature

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