Analogs of a formula of Lobachevsky for angle of parallelism on the hyperbolic plane of positive curvature
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 393-407.

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It is shown that on hyperbolic plane $\widehat {H}$ of positive curvature exists fifteen types of angles, angles of six types are measurable, angles of three types have the real measures. For quasiangles of parallelism, angles of quasiparallelism and angles of parallelism of the plane $\widehat{H}$ analogs of a formula of Lobachevsky are received.
Keywords: hyperbolic plane $\widehat{H}$ of positive curvature; quasiangle of parallelism; angle of quasiparallelism; angle of parallelism; analogs of a formula of Lobachevsky for angle of parallelism.
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L. N. Romakina. Analogs of a formula of Lobachevsky for angle of parallelism on the hyperbolic plane of positive curvature. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 393-407. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a28/

[1] N. V. Efimov, Vysshaya geometriya, Nauka, M., 1971

[2] B. A. Rozenfeld, Neevklidovy prostranstva, Nauka, M., 1969

[3] B. A. Rozefeld, M. P. Zamakhovskii, Geometriya grupp Li. Simmetricheskie, parabolicheskie i periodicheskie prostranstva, MTsNMO, M., 2003, 560 pp. | MR

[4] L. N. Romakina, “Razbieniya giperbolicheskoi ploskosti polozhitelnoi krivizny, porozhdennye pravilnym $n$-konturom”, Teoriya otnositelnosti, gravitatsiya i geometriya, Trudy Mezhd. konf. «Petrov 2010 Anniversary Sympozium on General Relativity and Gravitation» (Kazan, 1–6 noyabrya 2010 g.), Kazan. un-t, Kazan, 2010, 227–232

[5] L. N. Romakina, “Prostye razbieniya giperbolicheskoi ploskosti polozhitelnoi krivizny, porozhdennye $h$-lomanoi”, Matematika, Sovremennye problemy matematiki i mekhaniki, VI, no. 3, Izd-vo MGU, M., 2011, 131–138

[6] L. N. Romakina, “Analog mozaiki na giperbolicheskoi ploskosti polozhitelnoi krivizny”, Mekhanika. Matematika, Sb. nauch. tr., Izd-vo Sarat. un-ta, Saratov, 2010, 69–72 | MR

[7] L. N. Romakina, “Prostye razbieniya giperbolicheskoi ploskosti polozhitelnoi krivizny”, Matem. sb., 203:9 (2012), 83–116 | MR | Zbl

[8] L. N. Romakina, “Konechnye zamknutye 3(4)-kontury rasshirennoi giperbolicheskoi ploskosti”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 10:3 (2010), 14–26

[9] L. N. Romakina, “Konechnye zamknutye 5-kontury rasshirennoi giperbolicheskoi ploskosti”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 11:1 (2011), 38–49 | MR

[10] L. N. Romakina, “Ovalnye linii giperbolicheskoi ploskosti polozhitelnoi krivizny”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 12:3 (2012), 37–44 | MR

[11] L. N. Romakina, Geometrii koevklidovoi i kopsevdoevklidovoi ploskostei, OOO Izd-vo «Nauchnaya kniga», Saratov, 2008

[12] L. N. Romakina, “Opredelenie luchei, otrezkov i kvaziotrezkov razlichnogo tipa pryamykh pri postroenii klassicheskikh neevklidovykh geometrii na modelyakh Keli–Kleina”, 62-e Gertsenovskie chteniya, Mezhdun. konferentsiya, Sb. nauch. tr., Izd-vo RGPU im. A. I. Gertsena, Sankt-Peterburg, 2009, 103–109