Invariant Surfaces under Hyperbolic Translations in Hyperbolic Space

Mahmut Mak and Baki Karlığa

Journal of Applied Mathematics, 2014, vol. 2014, 1-12

Abstract:

We consider hyperbolic rotation ( ), hyperbolic translation ( ), and horocyclic rotation ( ) groups in , which is called Minkowski model of hyperbolic space. Then, we investigate extrinsic differential geometry of invariant surfaces under subgroups of in . 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 .

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:838564

DOI: 10.1155/2014/838564

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