Year 2021,
Volume: 9 Issue: 2, 298 - 309, 15.10.2021
Tuğba Mert
,
Mehmet Atceken
References
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329-336.
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12 (2019), 20-25.
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Density, Analele Stiintifice ale Universitatii Ovidius Constanta-Seria Matematica, 26 (2018), 99-108.
Some Special Ruled Surfaces in Hyperbolic 3-Space
Year 2021,
Volume: 9 Issue: 2, 298 - 309, 15.10.2021
Tuğba Mert
,
Mehmet Atceken
Abstract
In this paper, normal and binormal surfaces, a special class of ruled surfaces in hyperbolic 3-space, are discussed. These special surfaces are defined in hyperbolic 3-space and the types of these surfaces are introduced. The properties of these surfaces are given under the condition of being constant angle surface in hyperbolic 3-space.
References
- [1] M.Munteanu,A.Nistor,AnewapproachonconstantanglesurfacesinE3,TurkT.Math.,33(2009),169-178.
- [2] A.DiScala,G.Ruiz-Hernandez,HelixsubmanifoldsofEuclideanspace,Monatsh.Math.,157(2009),205-215.
- [3] G.Ruiz-Hernandez,Helixshadowboundaryandminimalsubmanifolds,IllinoisJ.Math.,52(2008),1385-1397.
- [4] P.Cermelli,A.DiScala,Constantanglesurfacesinliquidcrystals,Phylos.Magazine,87(2007),1871-1888.
- [5] F.Dillen,J.Fastenakels,J.VanderVekenandL.Vrancken,ConstantanglesurfacesinS2×R,Monaths.Math.,152(2007),89-96.
- [6] F.Dillen,M.Munteanu,ConstantanglesurfacesinH2×R,Bull.Braz.Math.Soc.,40(2009),85-97.
- [7] J.Fastenakels,M.MunteanuandJ.VanderVeken,ConstantanglesurfacesintheHeisenberggroup,ActaMath.Sinica(EnglishSeries),27(2011),
747-756.
- [8] R.Lopez,M.Munteanu,ConstantanglesurfacesinMinkowskispace,BulletinoftheBelgianMath.,18(2011),271-286.
- [9] T.Mert,ConstantAngleSurfacesinHyperbolicanddeSitterSpaces,GaziUniversityGraduateSchoolofNaturalandAppliedSciences,Ph.D.Thesis,
2014.
- [10] T.Mert.,B.Karlıg ̆a,ConstantAngleSpacelikeSurfaceinHyperbolicSpaceH3,J.Adv.Res.Appl.Math.,7(2015),89-102.
- [11] T.Mert.,B.Karlıg ̆a,OntheTimelikeSurfacewithConstantAngleinHyperbolikSpaceH3,CBUJ.ofSci.,12(2016),1-9.
- [12] T.Mert.,B.Karlıg ̆a,ConstantAngleSpacelikeSurfaceindeSitterSpaceS13,BoletimdaSociedadeParanaensedeMathematica,35(2017),79-93.
- [13] T.Mert.,B.Karlıg ̆a,TimelikeSurfacewithConstantAngleindeSitterSpaceS13,CumhuriyetUniversityFacultyofScienceJournal,37(2016),1-11.
- [14] T.Mert.,SpacelikeRuledSurfacesinHyperbolic3−Space,CumhuriyetSci.J.,39(2018),314-324.
- [15] A.Nistor,CerteinConstantAngleSurfacesConstructedonCurves,InternationalElectronicJournalofGeometry,4(2011),79-87.
- [16] S. Karakus, Certain Constant Angle Surfaces Constructed on Curves in Minkowski 3−Space, International Electronic Journal of Geometry, 11
(2018),37-47.
- [17] S.Izumıya,K.SajıandM.Takahashı,HorosphericalflatsurfacesinHyperbolic3-space,J.Math.Soc.Japan,87(2010),789-849.
- [18] C.Thas,AgaussmaponhypersurfacesofsubmanıfoldsınEuclıdeanspaces,J.KoreanMath.Soc.,16(1979),17-27.
- [19] S.Izumıya,D.PeıandM.Fuster,Thehorosphericalgeometryofsurfacesınhyperbolic4-spaces,IsraelJournalofMathematıcs,154(2006),361-379.
- [20] J.G.Ratcliffe,FoundationsofHyperbolicManifolds,Springer-VerlagNewYork,2006.
- [21] B.Karlıg ̆a.,OnTheGeneralizedStereographicProjection,BeitregezurAlgebraandGeometrieContributionstoAlgebraandGeometry,37(1996),
329-336.
- [22] O.G.Yıldız,M.Akyig ̆it,ConstructionsofTypeIIIHelicoidalSurfacesinMinkowskiSpacewithDensity,InternationalElectronicJournalofGeometry,
12 (2019), 20-25.
- [23] O.G.Yıldız,S.HızalandM.Akyig ̆it,TypeIHelicoidalSurfaceswithPrescribedWeightedMeanorGaussianCurvatureinMinkowskiSpacewith
Density, Analele Stiintifice ale Universitatii Ovidius Constanta-Seria Matematica, 26 (2018), 99-108.