Invariant Surfaces under Hyperbolic Translations in Hyperbolic Space
Copyright policy )Invariant Surfaces under Hyperbolic Translations in Hyperbolic Space
We consider hyperbolic rotation (G0), hyperbolic translation (G1), and horocyclic rotation (G2) groups inH3, which is called Minkowski model of hyperbolic space. Then, we investigate extrinsic differential geometry of invariant surfaces under subgroups ofG0inH3. 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 inH3.
- Gazi University Turkey
- Kırşehir Ahi Evran University Turkey
- Ahi Evran University Turkey
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), QA1-939, Hyperbolic and elliptic geometries (general) and generalizations, Minimal surfaces in differential geometry, surfaces with prescribed mean curvature, Mathematics
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), QA1-939, Hyperbolic and elliptic geometries (general) and generalizations, Minimal surfaces in differential geometry, surfaces with prescribed mean curvature, Mathematics
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