Invariant Surfaces under Hyperbolic Translations in Hyperbolic Space - Mahmut Mak; Baki Karlığa (Journal of Applied Mathematics, 2014)
We consider hyperbolic rotation (G0), hyperbolic translation (G1), and horocyclic rotation (G2) groups in H3, which is called Minkowski model of hyperbolic space. Then, we investigate extrinsic differential geometry of invariant surfaces under subgroups of G0 in H3. Also, we give explicit parametrization of these invariant surfaces with respect to constant hyperbolic curvature of profile curves. Finally, we obtain some corollaries for flat and minimal invariant surfaces which are associated with de Sitter and hyperbolic shape operator in H3.