Invariant Surfaces under Hyperbolic Translations in Hyperbolic Space
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 parametriz...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/838564 |
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| _version_ | 1850170820787175424 |
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| author | Mahmut Mak Baki Karlığa |
| author_facet | Mahmut Mak Baki Karlığa |
| author_sort | Mahmut Mak |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ac4ab97ce16146e49d7568c00c6c89e8 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-ac4ab97ce16146e49d7568c00c6c89e82025-08-20T02:20:23ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/838564838564Invariant Surfaces under Hyperbolic Translations in Hyperbolic SpaceMahmut Mak0Baki Karlığa1Department of Mathematics, Faculty of Arts and Sciences, Ahi Evran University, 40100 Kırşehir, TurkeyDepartment of Mathematics, Faculty of Arts and Sciences, Gazi University, 06500 Ankara, TurkeyWe 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.http://dx.doi.org/10.1155/2014/838564 |
| spellingShingle | Mahmut Mak Baki Karlığa Invariant Surfaces under Hyperbolic Translations in Hyperbolic Space Journal of Applied Mathematics |
| title | Invariant Surfaces under Hyperbolic Translations in Hyperbolic Space |
| title_full | Invariant Surfaces under Hyperbolic Translations in Hyperbolic Space |
| title_fullStr | Invariant Surfaces under Hyperbolic Translations in Hyperbolic Space |
| title_full_unstemmed | Invariant Surfaces under Hyperbolic Translations in Hyperbolic Space |
| title_short | Invariant Surfaces under Hyperbolic Translations in Hyperbolic Space |
| title_sort | invariant surfaces under hyperbolic translations in hyperbolic space |
| url | http://dx.doi.org/10.1155/2014/838564 |
| work_keys_str_mv | AT mahmutmak invariantsurfacesunderhyperbolictranslationsinhyperbolicspace AT bakikarlıga invariantsurfacesunderhyperbolictranslationsinhyperbolicspace |