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Isometric Lagrangian Immersion of Horocycles of the Hyperbolic Plane in Complex Space
L. A. Masal'tsev V. N. Karazin Kharkiv National University
Abstract:
We prove that there exists an isometric Lagrangian immersion of a horocycle of the hyperbolic plane in the complex space $\mathbb C^2$, and there exists an isometric Lagrangian immersion of a horoball of hyperbolic (Lobachevski) space $H^3$ in the complex space $\mathbb C^3$.
Keywords:
hyperbolic plane, horocycle, hyperbolic (Lobachevski) space, horoball, Lagrangian submanifold, Lagrangian immersion, Gauss–Codazzi–Ricci equations, Riemann connection, fiber bundle.
Received: 07.09.2006 Revised: 08.11.2007
Citation:
L. A. Masal'tsev, “Isometric Lagrangian Immersion of Horocycles of the Hyperbolic Plane in Complex Space”, Mat. Zametki, 84:4 (2008), 577–582; Math. Notes, 84:4 (2008), 538–543
Linking options:
https://www.mathnet.ru/eng/mzm4029https://doi.org/10.4213/mzm4029 https://www.mathnet.ru/eng/mzm/v84/i4/p577
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