Some Special Ruled Surfaces in Hyperbolic 3-Space

Tuğba Mert; Mehmet Atceken

Research Article

Year 2021, Volume: 9 Issue: 2, 298 - 309, 15.10.2021

Tuğba Mert Mehmet Atceken

Abstract

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.

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.

Keywords

Ruled Surface, Normal Surface, Binormal Surface

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.

There are 23 citations in total.

Details

Primary Language	English
Subjects	Engineering
Journal Section	Articles
Authors	Tuğba Mert Mehmet Atceken 0000-0001-8665-5945
Publication Date	October 15, 2021
Submission Date	February 6, 2020
Acceptance Date	October 31, 2021
Published in Issue	Year 2021 Volume: 9 Issue: 2

Cite

APA	Mert, T., & Atceken, M. (2021). Some Special Ruled Surfaces in Hyperbolic 3-Space. Konuralp Journal of Mathematics, 9(2), 298-309.
AMA	Mert T, Atceken M. Some Special Ruled Surfaces in Hyperbolic 3-Space. Konuralp J. Math. October 2021;9(2):298-309.
Chicago	Mert, Tuğba, and Mehmet Atceken. “Some Special Ruled Surfaces in Hyperbolic 3-Space”. Konuralp Journal of Mathematics 9, no. 2 (October 2021): 298-309.
EndNote	Mert T, Atceken M (October 1, 2021) Some Special Ruled Surfaces in Hyperbolic 3-Space. Konuralp Journal of Mathematics 9 2 298–309.
IEEE	T. Mert and M. Atceken, “Some Special Ruled Surfaces in Hyperbolic 3-Space”, Konuralp J. Math., vol. 9, no. 2, pp. 298–309, 2021.
ISNAD	Mert, Tuğba - Atceken, Mehmet. “Some Special Ruled Surfaces in Hyperbolic 3-Space”. Konuralp Journal of Mathematics 9/2 (October 2021), 298-309.
JAMA	Mert T, Atceken M. Some Special Ruled Surfaces in Hyperbolic 3-Space. Konuralp J. Math. 2021;9:298–309.
MLA	Mert, Tuğba and Mehmet Atceken. “Some Special Ruled Surfaces in Hyperbolic 3-Space”. Konuralp Journal of Mathematics, vol. 9, no. 2, 2021, pp. 298-09.
Vancouver	Mert T, Atceken M. Some Special Ruled Surfaces in Hyperbolic 3-Space. Konuralp J. Math. 2021;9(2):298-309.

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