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I ask the smooth embedding and immersion, not just C^1.
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  1. Can the complete simply-connected surface with constant Gauss curvature -1 be embedded smoothly in the 5-dimensional Euclidean space?

  2. Can the complete simply-connected surface with constant Gauss curvature -1 be immersed smoothly in the 4-dimensional Euclidean space?

  1. Can the complete simply-connected surface with constant Gauss curvature -1 be embedded in the 5-dimensional Euclidean space?

  2. Can the complete simply-connected surface with constant Gauss curvature -1 be immersed in the 4-dimensional Euclidean space?

  1. Can the complete simply-connected surface with constant Gauss curvature -1 be embedded smoothly in the 5-dimensional Euclidean space?

  2. Can the complete simply-connected surface with constant Gauss curvature -1 be immersed smoothly in the 4-dimensional Euclidean space?

Source Link
011000
011000
  • 81
  • 4

Embed the hyperbolic plane into Euclidean spaces

  1. Can the complete simply-connected surface with constant Gauss curvature -1 be embedded in the 5-dimensional Euclidean space?

  2. Can the complete simply-connected surface with constant Gauss curvature -1 be immersed in the 4-dimensional Euclidean space?