Geodesic
Isometric Lagrangian Immersion of Horocycles of the Hyperbolic Plane in Complex Space
Matematičeskie zametki, Tome 84 (2008) no. 4, pp. 577-582.

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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, hyperbolic (Lobachevski) space, horoball, Lagrangian submanifold, Lagrangian immersion, Gauss–Codazzi–Ricci equations, Riemann connection, fiber bundle.
Mots-clés : horocycle 
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L. A. Masal'tsev. Isometric Lagrangian Immersion of Horocycles of the Hyperbolic Plane in Complex Space. Matematičeskie zametki, Tome 84 (2008) no. 4, pp. 577-582. http://geodesic.mathdoc.fr/item/MZM_2008_84_4_a8/

[1] N. V. Efimov, “Nepogruzhaemost poluploskosti Lobachevskogo”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 30:2 (1975), 83–86 | MR | Zbl

[2] E. G. Poznyak, “Izometricheskoe pogruzhenie v $E^3$ nekotorykh nekompaktnykh oblastei ploskosti Lobachevskogo”, Matem. sb., 102:1 (1977), 3–12 | MR | Zbl

[3] E. R. Rozendorn, “Poverkhnosti otritsatelnoi krivizny”, Geometriya – 3, Itogi nauki i tekhniki. Sovrem.problemy matem. Fundam. napr., 48, VINITI, M., 1989, 98–195 | MR | Zbl

[4] I. Kh. Sabitov, “Ob izometricheskikh pogruzheniyakh ploskosti Lobachevskogo v $E^4$”, Sib. matem. zhurn., 30:5 (1989), 179–186 | MR | Zbl

[5] S. B. Kadomtsev, “Nevozmozhnost nekotorykh spetsialnykh izometricheskikh pogruzhenii prostranstv Lobachevskogo”, Matem. sb., 107:2 (1978), 175–198 | MR | Zbl

[6] Zh. Kaidasov, E. V. Shikin, “Ob izometricheskom pogruzhenii v $E^3$ vypukloi oblasti ploskosti Lobachevskogo, soderzhaschei dva orikruga”, Matem. zametki, 39:4 (1986), 612–617 | MR | Zbl

[7] Yu. A. Aminov, “O funktsionalno-vyrozhdennykh pogruzheniyakh ploskosti Lobachevskogo v $E^4$”, Ukr. geom. sb., 1990, no. 33, 8–18 | MR | Zbl

[8] T. Garibe, “Dvumernye poverkhnosti s postoyannoi vneshnei geometriei v $E^5$”, Ukr. geom. sb., 1982, no. 25, 11–22 | MR | Zbl

[9] J. D. Moore, J.-M. Morvan, “On isometric Lagrangian immersions”, Illinois J. Math., 45:3 (2001), 833–849 | MR | Zbl

[10] K. Yano, M. Kon, $CR$-podmnogoobraziya v kelerovom i sasakievom mnogoobraziyakh, Nauka, M., 1990 | MR | Zbl

[11] Yu. A. Aminov, Geometriya podmnogoobrazii, Naukova dumka, Kiev, 2002 | Zbl