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Surfaces with constant mean curvature in Sol geometry

Authors
Journal
Differential Geometry and its Applications
0926-2245
Publisher
Elsevier
Publication Date
Volume
29
Identifiers
DOI: 10.1016/j.difgeo.2011.04.047
Keywords
  • Sol3
  • Helicoidal Surface
  • Mean Curvature
  • Minimal Surface
  • Invariant Surface
  • Translation Surface
Disciplines
  • Mathematics

Abstract

Abstract Among the eight geometries of Thurston, Sol 3 is the space with the smallest number of isometries, for example, there are no rotations. In this work, we classify all surfaces with constant mean curvature that either are invariant by a 1-parameter group of isometries or are the product of two planar curves.

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