Timelike Surfaces With Constant Angle In De Sitter Space

Tuğba Mert; Baki Karlığa

doi:10.17776/csj.84703

Timelike Surfaces With Constant Angle In De Sitter Space

Year 2016, Volume: 37 Issue: 1, 1 - 11, 06.04.2016

Tuğba Mert Baki Karlığa

https://doi.org/10.17776/csj.84703

Abstract

Abstract. In this paper; using the angle between unit normal vector eld of
surfaces and a xed spacelike axis in Minkowski space, we develop a special class of timelike surface which is called constant timelike angle surfaces in de Sitter space.

Keywords and phrases. Constant angle surfaces, de Sitter space, Helix, Timelike

Özet. Bu çalışmada, yüzeyin birim normal vektör alanı ve R4'de sabit bir uzaysal eksen arasındaki açı kullanılarak, de-Sitter uzayında sabit zamansal açılı yüzeyler olarak adlandırılan zamansal yüzeylerin özel bir sınıfı geliştirilmiştir.

Anahtar Kelimeler: Sabit açılı yüzeyler, de-Sitter uzayı, Helis, zamansal

References

R. Lopez, M.I. Munteanu, Constant angle surfaces in Minkowski space, Bulletin of the Belgian Math. So. Simon Stevin, Vo.18 (2011) 2, (271-286).
S.Izumıya, K.Sajı, M.Takahashı, Horospherical flat surfaces in Hyperbolic 3-space, J.Math.Soc.Japan, Vol.87 (2010), (789-849).
S.Izumıya, D.Peı, M.D.C.R. Fuster, The horospherical geometry of surfaces ın hyperbolic 4- spaces, Israel Journal of Mathematıcs, Vol.154 (2006), (361-379).
C.Thas, A gauss map on hypersurfaces of submanıfolds ın Euclıdean spaces, J.Korean Math.Soc., Vol.16, No.1, (1979).
S.Izumıya, D.Peı, T.Sano, Sıngularities of hyperbolic gauss map, London Math.Soc. Vol.3 (2003), (485-512).
M.I.Munteanu, A.I.Nistor, A new approach on constant angle surfaces in E , Turk T.Math. 3 , Turk T.Math.
Vol.33 (2009), (169-178).
C.Takızawa, K.Tsukada , Horocyclic surfaces in hyperbolic 3-space, Kyushu J.Math. Vol.63 (2009), (269-284).
S.Izumıya, M.D.C.R. Fuster, The horospherical Gauss-Bonnet type theorem in hyperbolic space, J.Math.Soc.Japan, Vol.58 (2006), (965-984).
B. O'Neill, Semi-Riemannıan Geometry with applications to relativity, Academic Press, New York, 1983.
W.Fenchel , Elementary Geometry in Hyperbolic Space, Walter de Gruyter , New York , 1989.
J.G.Ratcliffe, Foundations of Hyperbolic Manifolds, Springer 1948.
P.Cermelli, A.J. Di Scala, Constant angle surfaces in liquid crystals, Phylos. Magazine,Vol.87 (2007),(1871-1888).
A.J. Di Scala, G. Ruiz-Hernandez, Helix submanifolds of Euclidean space, Monatsh. Math. DOI 10.1007 / s00605-008-0031-9.
G.Ruiz-Hernandez, Helix, shadow boundary and minimal submanifolds, Illinois J. Math. Vol.52 (2008),(1385-1397).
F. Dillen, J. Fastenakels, J. Van der Veken, L. Vrancken, Constant angle surfaces in S 2 R , Monaths. Math. , Vol.152 (2007), (89-96).
F. Dillen and M. I. Munteanu, Constant angle surfaces in H 2
R, Bull. Braz. Math. soc. , Vol.40 (2009), (85-97).
J. Fastenakels, M. I: Munteanu , J. Van der Veken, Constant angle surfaces in the Heisenberg group, Acta Math. Sinica (English Series) Vol.27 (2011), (747-756).
R.Lopez, Differantial Geometry of Curves and Surfaces in Lorentz-Minkowski space, arXiv: 0810.3351 (2008).
Mert.T, Karliğa.B, Constant Angle Spacelike Surface in Hyperbolic Space H, J. Adv. Res. Appl. Math., 7(2015), no 2, (89-102).
Mert.T, Karliğa.B, Constant Angle Spacelike Surface in de Sitter Space S, Boletim da 3, Boletim da 1 Sociedade Paranaense de Mathematica (Accepted).
Mert.T, Karliğa.B, On The Timelike Surface with Constant Angle in Hyperbolic Space H, 3, CBU Journal of Science (Accepted).
M. Kasedou , Spacelike submanifolds in de sitter space, demonstratio Mathematica , Vol.XLIII (2010) , 2.

De-Sitter Uzayında Sabit Açılı Zamansal Yüzeyler 4de sabit bir uzaysal eksen arasındaki açıyı kullanarak, de

Year 2016, Volume: 37 Issue: 1, 1 - 11, 06.04.2016

Tuğba Mert Baki Karlığa

https://doi.org/10.17776/csj.84703

Abstract

Sitter uzayında sabit zamansal açılı yüzeyler olarak adlandırılan zamansal yüzeylerin özel bir sınıfı geliştirilmiştir

Keywords

Sabit açılı yüzeyler, de-Sitter uzayı, Helis, zamansal yüzeyler

References

R. Lopez, M.I. Munteanu, Constant angle surfaces in Minkowski space, Bulletin of the Belgian Math. So. Simon Stevin, Vo.18 (2011) 2, (271-286).
S.Izumıya, K.Sajı, M.Takahashı, Horospherical flat surfaces in Hyperbolic 3-space, J.Math.Soc.Japan, Vol.87 (2010), (789-849).
S.Izumıya, D.Peı, M.D.C.R. Fuster, The horospherical geometry of surfaces ın hyperbolic 4- spaces, Israel Journal of Mathematıcs, Vol.154 (2006), (361-379).
C.Thas, A gauss map on hypersurfaces of submanıfolds ın Euclıdean spaces, J.Korean Math.Soc., Vol.16, No.1, (1979).
S.Izumıya, D.Peı, T.Sano, Sıngularities of hyperbolic gauss map, London Math.Soc. Vol.3 (2003), (485-512).
M.I.Munteanu, A.I.Nistor, A new approach on constant angle surfaces in E , Turk T.Math. 3 , Turk T.Math.
Vol.33 (2009), (169-178).
C.Takızawa, K.Tsukada , Horocyclic surfaces in hyperbolic 3-space, Kyushu J.Math. Vol.63 (2009), (269-284).
S.Izumıya, M.D.C.R. Fuster, The horospherical Gauss-Bonnet type theorem in hyperbolic space, J.Math.Soc.Japan, Vol.58 (2006), (965-984).
B. O'Neill, Semi-Riemannıan Geometry with applications to relativity, Academic Press, New York, 1983.
W.Fenchel , Elementary Geometry in Hyperbolic Space, Walter de Gruyter , New York , 1989.
J.G.Ratcliffe, Foundations of Hyperbolic Manifolds, Springer 1948.
P.Cermelli, A.J. Di Scala, Constant angle surfaces in liquid crystals, Phylos. Magazine,Vol.87 (2007),(1871-1888).
A.J. Di Scala, G. Ruiz-Hernandez, Helix submanifolds of Euclidean space, Monatsh. Math. DOI 10.1007 / s00605-008-0031-9.
G.Ruiz-Hernandez, Helix, shadow boundary and minimal submanifolds, Illinois J. Math. Vol.52 (2008),(1385-1397).
F. Dillen, J. Fastenakels, J. Van der Veken, L. Vrancken, Constant angle surfaces in S 2 R , Monaths. Math. , Vol.152 (2007), (89-96).
F. Dillen and M. I. Munteanu, Constant angle surfaces in H 2
R, Bull. Braz. Math. soc. , Vol.40 (2009), (85-97).
J. Fastenakels, M. I: Munteanu , J. Van der Veken, Constant angle surfaces in the Heisenberg group, Acta Math. Sinica (English Series) Vol.27 (2011), (747-756).
R.Lopez, Differantial Geometry of Curves and Surfaces in Lorentz-Minkowski space, arXiv: 0810.3351 (2008).
Mert.T, Karliğa.B, Constant Angle Spacelike Surface in Hyperbolic Space H, J. Adv. Res. Appl. Math., 7(2015), no 2, (89-102).
Mert.T, Karliğa.B, Constant Angle Spacelike Surface in de Sitter Space S, Boletim da 3, Boletim da 1 Sociedade Paranaense de Mathematica (Accepted).
Mert.T, Karliğa.B, On The Timelike Surface with Constant Angle in Hyperbolic Space H, 3, CBU Journal of Science (Accepted).
M. Kasedou , Spacelike submanifolds in de sitter space, demonstratio Mathematica , Vol.XLIII (2010) , 2.

There are 24 citations in total.

Details

Journal Section	Natural Sciences Research Article
Authors	Tuğba Mert Baki Karlığa This is me
Publication Date	April 6, 2016
Published in Issue	Year 2016 Volume: 37 Issue: 1

Cite

APA	Mert, T., & Karlığa, B. (2016). Timelike Surfaces With Constant Angle In De Sitter Space. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, 37(1), 1-11. https://doi.org/10.17776/csj.84703
AMA	Mert T, Karlığa B. Timelike Surfaces With Constant Angle In De Sitter Space. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. April 2016;37(1):1-11. doi:10.17776/csj.84703
Chicago	Mert, Tuğba, and Baki Karlığa. “Timelike Surfaces With Constant Angle In De Sitter Space”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 37, no. 1 (April 2016): 1-11. https://doi.org/10.17776/csj.84703.
EndNote	Mert T, Karlığa B (April 1, 2016) Timelike Surfaces With Constant Angle In De Sitter Space. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 37 1 1–11.
IEEE	T. Mert and B. Karlığa, “Timelike Surfaces With Constant Angle In De Sitter Space”, Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 37, no. 1, pp. 1–11, 2016, doi: 10.17776/csj.84703.
ISNAD	Mert, Tuğba - Karlığa, Baki. “Timelike Surfaces With Constant Angle In De Sitter Space”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 37/1 (April 2016), 1-11. https://doi.org/10.17776/csj.84703.
JAMA	Mert T, Karlığa B. Timelike Surfaces With Constant Angle In De Sitter Space. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2016;37:1–11.
MLA	Mert, Tuğba and Baki Karlığa. “Timelike Surfaces With Constant Angle In De Sitter Space”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 37, no. 1, 2016, pp. 1-11, doi:10.17776/csj.84703.
Vancouver	Mert T, Karlığa B. Timelike Surfaces With Constant Angle In De Sitter Space. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2016;37(1):1-11.