Classification of Conformal Surfaces of Revolution in Hyperbolic 3-Space
Abstract
In this paper, we classify conformal surfaces of revolution in hyperbolic
3-space $\mathbb{H}^{3}(-c^{2})$ satisfying an equation in terms of the position vector field and the Laplace operators with respect to the first,
the second and the third fundamental forms of the surface.
Keywords
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E. Abbena, S. Salamon and A. Gray: Modern Differential Geometry of Curves and Surfaces with Mathematica. CRC Press. 92 (2006).
L. J. Alias, A. Ferrandez and P. Lucas: Surfaces in the 3-dimensional Lorentz-Minkowski space satisfying ∆x = Ax + B. Pacific J. Math. 156 (1992), 201–208.
C. Baikoussis and L. Verstraelen: On the Gauss map of helicoidal surfaces. Rend. Sem. Math. Messina Ser. II 2(16) (1993), 31–42.
M. Bekkar and H. Zoubir: Surfaces of Revolution in the 3-Dimensional Lorentz-Minkowski Space Satisfying ∆x i = λ i x i . Int. J. Contemp. Math. Sciences. 3(24) (2008), 1173 - 1185.
S. M. Choi: On the Gauss map of surfaces of revolution in a 3-dimensional Minkowski space. Tsukuba J. Math. 19 (1995), 351–367.
M. Choi, Y. H. Kim and D. W. Yoon: Some classification of surfaces of revolution in Minkowski 3-space. J. Geom. 104 (2013), 85–106.
.B Y. Chen: A report on submanifold of finite type. Soochow J. Math. 22 (1996), 117–337.
F. Dillen, J. Pas and L. Vertraelen: On surfaces of finite type in Euclidean
-space. Kodai Math. J. 13 (1990), 10–21.
F. Dillen, J. Pas and L. Vertraelen: On the Gauss map of surfaces of revolution. Bull. Inst. Math. Acad. Sinica. 18 (1990), 239–246.
O. J. Garay: n extension of Takahashi’s theorem. Geom. Dedicata. 34 (1990), 105–112.
E. Guler and O. Kisi: The Second Laplace-Beltrami Operator on Rotational Hy-
persurfaces in the Euclidean 4-Space. Mathematica Aeterna. 8(1) (2018), 1–12.
G. Kaimakamis, B. Papantoniou and K Petoumenos: Surfaces of revolution in the 3-dimensional Lorentz-Minkowski space satisfying ∆ III r = Ar. Bull.Greek Math.
Soc. 50 (2005), 75–90.
E. P. Lambert: Lorentz invariant spacelike surfaces of constant mean curvature in anti de sitter 3-space. Msc. Thesis, The University of Southern Mississippi, 2015.
S. Lee: Spacelike surfaces of constant mean curvature one in de Sitter 3-space. Illinois Journal of Mathematics. 49(1) (2005), 63–98.
S. Lee and K. Zarske : Surfaces of revolution with constant mean curvature in Hyperbolic 3-space. Differential Geometry - Dynamical Systems (DGDS). 16 (2014),
–218.
S. Lee and J. Martin : Timelike surfaces of revolution with constant mean curvature in de sitter 3-space. International Electronic Journal of Geometry (IEJG). 8 (1) (2015), 116–127.
B. Senoussi and M. Bekk r : Helicoidal surfaces with ∆ J r = Ar in 3-dimensional Euclidean space. Stud. Univ. Babes-Bolyai Math. 60(3) (2015), 437–448.
T. Takahashi : Minimal immersions of Riemannian manifolds. J. Math. Soc. Japan. 18 (1996), 380–385.
J. Vrˇ sek and M. Láviˇ cka: Determining surfaces of revolution from their implicit equations. Journal of Computational and Applied Mathematics. 290 (2015), 125–135.
DOI: https://doi.org/10.22190/FUMI2002333Y
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