호남수학학술지 (Honam Mathematical Journal)

  • 제46권2호
  • /
  • Pages.249-266
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  • 2024
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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SURFACES WITH CONSTANT GAUSSIAN AND MEAN CURVATURES N THE ANTI-DE SITTER SPACE ℍ31

  • Ugur Dursun (Department of Mathematics, Isik University)
  • 투고 : 2023.09.20
  • 심사 : 2024.01.23
  • 발행 : 2024.06.25
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초록

In this work, we study time-like and space-like surfaces invariant by a group of translation isometries of the half-space model ℋ31 of the anti-de Sitter space ℍ31 . We determine all such surfaces with constant mean curvature and constant Gaussian curvature. We also obtain umbilical surfaces of ℋ31.

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참고문헌

  1. L. Belarbi, Surfaces with constant extrinsically Gaussian curvature in the Heisenberg group, Ann. Math. Inform. 50 (2019), 5-17.
  2. J. Danciger, Geometric transition: from hyperbolic to AdS geometry, PhD thesis, Stanford University, 2011.
  3. T. Hasanis and R. Lopez, Classification and construction of minimal translation surfaces in Euclidean space, Results Math. 75 (2020), Article No 2 (22 pages).
  4. T. Hasanis and R. Lopez, Translation surfaces in Euclidean space with constant Gaussian curvature, Commun. Anal. Geom. 29 (2021), 1415-1447.
  5. J. Inoguchi, M. Ionel, and S. Lee, Flat Lorentz surfaces in anti-de Sitter 3-space and Gravitational Instantons, Int. J. Geom. Methods Mod. Phys. 13 (2016), No: 1650012 (19 pages).
  6. J. Inoguchi, R. Lopez, and M. I. Munteanu, Minimal translation surfaces in the Heisenberg group Nil3, Geom. Dedicata 161 (2012), 221-231.
  7. J. P. Lambert, Lorentz invariant spacelike surfaces of constant mean curvature in anti-de Sitter 3-space, Master's Theses, 119 (2015). https://aquila.usm.edu/masters_theses/119.
  8. H. Liu, Translation surfaces with constant mean curvature in 3-dimensional spaces, J. Geom. 64 (1999), 141-149.
  9. R. Lopez, Parabolic surfaces in hyperbolic space with constant Gaussian curvature, Bull. Belg. Math. Soc. Simon Stevin 16 (2009), 337-349.
  10. R. Lopez, Minimal translation surfaces in hyperbolic space, Beitr. Algebra Geom. 52 (2011), 105-112.
  11. R. Lopez and M. I. Munteanu, Minimal translation surfaces in Sol3, J. Math. Soc. Japan 64 (2012), 985-1003.
  12. K. Nomizu, The Lorentz-Poincare metric on the upper half-space and its extension, Hokkaido Math. J. 11 (1982), 253-261.
  13. C. Ramis and M. I. Munteanu, Minimal translation surfaces in the three-dimensional Heisenberg group, Filomat 33 (2019), 1583-1592.
  14. A. Seppi and E. Trebeschi, The half-space model of pseudo-hyperbolic space, Developments in Lorentzian Geometry, Feb 2021, Cordoba, Spain. pp. 285-313. hal-03421097v2.
  15. Z. M. Sipus, Translation surfaces of constant curvatures in a simply isotropic space, Period Math. Hung. 68 (2014), 160-175.
  16. A. Tamburelli, Fenchel-Nielsen coordinates on the augmented moduli space of anti-de Sitter structures, Math. Z. 297 (2021), 1397-1419.
  17. D. W. Yoon, Minimal translation surfaces in ℍ2×ℝ, Taiwan. J. Math. 17 (2013), 1545-1556.