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.

UDC: 514

Received: 07.09.2006
Revised: 08.11.2007

DOI: 10.4213/mzm4029

 English version: Mathematical Notes, 2008, 84:4, 538–543

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