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1999 | 79 | 1 | 17-23
Tytuł artykułu

Isometric immersions of the hyperbolic space $H^n(-1)$ into $H^{n+1}(-1)$

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We transform the problem of determining isometric immersions from $H^n(-1)$ into $H^{n+1}(-1)$ into that of solving equations of degenerate Monge-Ampère type on the unit ball $B^n(1)$. By presenting one family of special solutions to the equations, we obtain a great many noncongruent examples of such isometric immersions with or without umbilic set.
Rocznik
Tom
79
Numer
1
Strony
17-23
Opis fizyczny
Daty
wydano
1999
otrzymano
1997-09-30
poprawiono
1998-04-25
Twórcy
autor
  • Postdoctoral Station of Mathematics, Hangzhou University, Hangzhou 310028, Zhejiang, People's Republic of China
Bibliografia
  • [1] K. Abe, Applications of a Riccati type differential equation to Riemannian manifolds with totally geodesic distributions, Tôhoku Math. J. 25 (1973), 425-444.
  • [2] K. Abe and A. Haas, Isometric immersions of $H^n$ into $H^n+1$, in: Proc. Sympos. Pure Math. 54, Part 3, Amer. Math. Soc., 1993, 23-30.
  • [3] K. Abe, H. Mori and H. Takahashi, A parametrization of isometric immersions between hyperbolic spaces, Geom. Dedicata 65 (1997), 31-46.
  • [4] D. Ferus, Totally geodesic foliations, Math. Ann. 188 (1970), 313-316.
  • [5] D. Ferus, On isometric immersions between hyperbolic spaces, ibid. 205 (1973), 193-200.
  • [6] P. Hartman and L. Nirenberg, On spherical image maps whose Jacobians do not change sign, Amer. J. Math. 81 (1959), 901-920.
  • [7] Z. J. Hu and G. S. Zhao, Classification of isometric immersions of the hyperbolic space $H^2$ into $H^3$, Geom. Dedicata 65 (1997), 47-57.
  • [8] Z. J. Hu and G. S. Zhao, Isometric immersions from the hyperbolic space $H^2(-1)$ into $H^3(-1)$, Proc. Amer. Math. Soc. 125 (1997), 2693-2697.
  • [9] A. M. Li, Spacelike hypersurfaces with constant Gauss-Kronecker curvature in Minkowski space, Arch. Math. (Basel) 64 (1995), 534-551.
  • [10] W. Massey, Spaces of Gaussian curvature zero in Euclidean $3$-space, Tôhoku Math. J. 14 (1962), 73-79.
  • [11] K. Nomizu, Isometric immersions of the hyperbolic plane into the hyperbolic space, Math. Ann. 205 (1973), 181-192.
  • [12] V. Oliker and U. Simon, Codazzi tensors and equations of Monge-Ampère type on compact manifolds of constant sectional curvature, J. Reine Angew. Math. 342 (1983), 35-65.
  • [13] B. O'Neill and E. Stiel, Isometric immersions of constant curvature manifolds, Michigan Math. J. 10 (1963), 335-339.
  • [14] B. G. Wachsmuth, On the Dirichlet problem for the degenerate real Monge-Ampère equation, Math. Z. 210 (1992), 23-35.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-cmv79z1p17bwm
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