Open Access
2014 Invariant Surfaces under Hyperbolic Translations in Hyperbolic Space
Mahmut Mak, Baki Karlığa
J. Appl. Math. 2014: 1-12 (2014). DOI: 10.1155/2014/838564


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.


Download Citation

Mahmut Mak. Baki Karlığa. "Invariant Surfaces under Hyperbolic Translations in Hyperbolic Space." J. Appl. Math. 2014 1 - 12, 2014.


Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07131909
MathSciNet: MR3283439
Digital Object Identifier: 10.1155/2014/838564

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
Back to Top