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Invariant Surfaces in Homogeneous Space Sol with Constant Curvature

Shavvakh, Mohammad Hossein | 2015

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 47955 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Fanai, Hamid Reza
  7. Abstract:
  8. In Twentieth century, W.P. Thurston formulated a geometric conjecture for three dimensional manifolds, namely every compact orientablethree-manifold admits a canonical decomposition into pieces, each of them having a canonical geometric structure from the following eight maximal and simply connected homogeneous Riemannian spaces among Sol spaces.A surface in homogeneous space Sol is said to be an invariant surface if it is invariant under some of the two one-parameter groups of isometries of the ambient space whose fix point sets are totally geodesic surfaces. In this work we study invariant surfaces that satisfy a certain condition on their curvatures. We classify invariant surfaces with constant mean curvature and constant Gaussian curvature. Also, we characterize invariant surfaces that satisfy a linear Weingarten relation
  9. Keywords:
  10. Homogeneous Space ; Sol3 Space ; Invariant Surfaces ; Constant Curvature ; Gaussian Curvature

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