We give a reduction procedure to determine (locally) the surfaces with constant Gauss curvature in a three-dimensional manifold which are invariant under the action of a one-parameter subgroup of the isometry group of the ambient space. We apply this procedure to describe the invariant surfaces with constant Gauss curvature in H^2 × R and in H_3 .
Invariant surfaces of a three-dimensional manifold with constant gauss curvature
MONTALDO, STEFANO;ONNIS I. I.
2005
Abstract
We give a reduction procedure to determine (locally) the surfaces with constant Gauss curvature in a three-dimensional manifold which are invariant under the action of a one-parameter subgroup of the isometry group of the ambient space. We apply this procedure to describe the invariant surfaces with constant Gauss curvature in H^2 × R and in H_3 .
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