Rotationally invariant constant Gauss curvature surfaces in Berger spheres

  title={Rotationally invariant constant Gauss curvature surfaces in Berger spheres},
  author={Francisco Torralbo and Joeri Van der Veken},
  journal={arXiv: Differential Geometry},
We give a full classification of complete rotationally invariant surfaces with constant Gauss curvature in Berger spheres: they are either Clifford tori, which are flat, or spheres of Gauss curvature $K \geq K_0$ for a positive constant $K_0$, which we determine explicitly and depends on the geometry of the ambient Berger sphere. For values of $K_0 \leq K \leq K_P$, for a specific constant $K_P$, it was not known until now whether complete constant Gauss curvature $K$ surfaces existed in Berger… Expand

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