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Classification of Minimal Translation Surfaces in Euclidean Space

Samadpour, Sina | 2023

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 56471 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Fanai, Hamid Reza
  7. Abstract:
  8. The main goal of this thesis is to classify minimal translation surfaces of three-dimensional Euclidean space. In pursuing that, a method will be introduced that constructs explicit examples. A translation surface is the sum of two regular curves α and β. A minimal surface is a surface, with zero mean curvature. Will be shown that besides the know examples (plane and surfaces of Scherk type) any minimal translation surfaces can be described Ψ(s, t) = α(s)+α(t) , where α is the unit speed curve and its curvature κα is a positive solution of (y ′ ) 2 + y 4 + c3y 2 + c 2 1 y −2 + c1c2 = 0 and its torsion is τ (s) = c1/κ(s) 2 . the above coefficients and their relations will be described
  9. Keywords:
  10. Translation Surfaces ; Minimal Surfaces ; Euclidean Space ; Cheng-Yau Operator ; Scherk Type Surfaces

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