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Matematicheskie Zametki, 2008, Volume 84, Issue 4, Pages 577–582
DOI: https://doi.org/10.4213/mzm4029 (Mi mzm4029) 		 
Isometric Lagrangian Immersion of Horocycles of the Hyperbolic Plane in Complex Space

L. A. Masal'tsev

V. N. Karazin Kharkiv National University
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DOI: https://doi.org/10.4213/mzm4029
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
English version:
Mathematical Notes, 2008, Volume 84, Issue 4, Pages 538–543
DOI: https://doi.org/10.1134/S0001434608090253
Bibliographic databases:
UDC: 514
Language: Russian
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
Citation in format AMSBIB
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