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Mat. Zametki, 2008, Volume 84, Issue 4, Pages 577–582 (Mi mz4029)  

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

DOI: https://doi.org/10.4213/mzm4029

Full text: PDF file (405 kB)
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English version:
Mathematical Notes, 2008, 84:4, 538–543

Bibliographic databases:

UDC: 514
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

Citation in format AMSBIB
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\paper Isometric Lagrangian Immersion of Horocycles of the Hyperbolic Plane in Complex Space
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\yr 2008
\vol 84
\issue 4
\pages 577--582
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