Hiperbolik Uzayda Sabit Açılı Zamansal Yüzeyler Üzerine

Bu çalışmada, yüzeyin birim normal vektör alanı ile4 R1de sabit uzaysal bir doğrultu ile sabit birzamansal açı yapan yüzeyler çalışılmıştır.3x M H : ?uzaysal bir immersiyon ve? , Myüzeyinin birim normal vektörü olsun. EğerMyüzeyi üzerinde? ?? ,U ?zamansal açısı sabit olacakşekilde sabit bir uzaysalUdoğrultusu varsa,Myüzeyine3 Hhiperbolik uzayında sabit uzaysaleksenli zamansal açılı yüzey denir. Ayrıca hiperbolik uzayda sabit açılı yüzey olma koşullarıbelirlenmiş ve bu yüzeylerin değişmezleri araştırılmıştır

On the Timelike Surface with Constant Angle in Hyperbolic Space H3

In this paper , we study constant timelike angle surface whose unit normal vector field make constanttimelike with a fixed spacelike axis in4 R1in Hyperbolic space3 H . Let3x M H : ? be a spacelikeimmersion and let?be a unit normal vector field toM. If there exists spacelike directionUsuch that timelike angle? ?? ,U ?is constant onM, thenMis called constant timelike angle surfaceswith spacelike axis in3 H . Also, conditions being a constant angle surface in3 Hhave been determinedand invariants of these surfaces have been investigated.

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[1] Lopez, R.; Munteanu, M. Constant angle surfaces in Minkowski space. Bulletin of the Belgian Math. So. Simon Stevin. 2011; 18(2), 271-286.
[2] Izumıya, S.; Sajı, K.; Takahashı, M. Horospherical flat surfaces in Hyperbolic 3-space. J.Math.Soc.Japan. 2010; 87, 789-849.
[3] Izumıya, S.; Peı, D.; Fuster, M. The horospherical geometry of surfaces ın hyperbolic 4-spaces. Israel Journal of Mathematıcs. 2006; 154, 361-379.
[4] Thas, C. A gauss map on hypersurfaces of submanıfolds ın Euclıdean spaces. J.Korean Math.Soc. 1979; 16, 17-27.
[5] Izumıya, S.; Peı, D.; Sano, T. Sıngularities of hyperbolic gauss map. London Math.Soc. 2003; 3, 485-512.
[6] Munteanu, M.; Nistor, A. A new approach on constant angle surfaces in 3 E . Turk T.Math. 2009; 33, 169-178.
[7] Takızawa, C.; Tsukada, K. Horocyclic surfaces in hyperbolic 3-space. Kyushu J.Math. 2009; 63, 269-284.
[8] Izumıya, S.; Fuster, M. The horospherical Gauss-Bonnet type theorem in hyperbolic space. J.Math.Soc.Japan. 2006; 58, 965-984.
[9] O'Neill, B. Semi-Riemannıan Geometry with applications to relativity. Academic Press, New York, 1983.
[10] Fenchel, W. Elementary Geometry in Hyperbolic Space. Walter de Gruyter, New York, 1989.
[11] Ratcliffe, J.G. Foundations of Hyperbolic Manifolds, Springer, 1994.
[12] Cermelli, P.; Di Scala, A. Constant angle surfaces in liquid crystals. Phylos. Magazine. 2007; 87, 1871-1888.
[13] Di Scala, A.; Ruiz-Hernandez, G. Helix submanifolds of Euclidean space. Monatsh. Math. 2009; 157, 205-215.
[14] Ruiz-Hernandez, G. Helix shadow boundary and minimal submanifolds. Illinois J. Math. 2008; 52, 1385-1397.
[15] Dillen, F.; Fastenakels, J.; Van der Veken, J.; Vrancken, L. Constant angle surfaces in 2 S R? . Monaths. Math. 2007; 152, 89-96.
[16] Dillen F.; Munteanu, M. Constant angle surfaces in 2 H R? . Bull. Braz. Math. soc. 2009; 40, 85-97.
[17] Fastenakels, J.; Munteanu, M.; Van der Veken, J. Constant angle surfaces in the Heisenberg group. Acta Math. Sinica (English Series). 2011; 127, 747-756.
[18] Lopez, R. Differantial Geometry of Curves and Surfaces in Lorentz-Minkowski space, 2008; 0810-3351.
[19] Mert, T.; Karlığa,B. Constant Angle Spacelike Surface in Hyperbolic 3-Space. J.Adv. Res. Appl. Math. 2015; 7, 89-102.
[20] Mert, T.; Karlığa, B. Constant Angle Spacelike Surface in de-Sitter space 31 S . Boletim da Sociedade Paranaense de Mathematica. 2016; Accepted.
[21] Buosi, M.; Izumiya, S.; Soares Ruas, M. Total absolute horospherical curvature of submanifolds in hyperbolic space. Advances in Geometry. 2010; 10(4), 603-620.