Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Romakina L. N. Parabolic parallelograms of the plane Ĥ. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 1, pp. 20-28. DOI: 10.18500/1816-9791-2014-14-1-20-28, EDN: SCSSQR

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
25.03.2014
Full text:
download
(downloads: 247)
Language: 
Russian
Heading: 
Mathematics
UDC: 
514.133
DOI: 
10.18500/1816-9791-2014-14-1-20-28
EDN: 
SCSSQR

Parabolic parallelograms of the plane Ĥ

Autors: 
Romakina Lyudmila Nikolaevna, Saratov State University
Abstract: 

Parabolic parallelograms on a Hyperbolic Plane Hˆ with the positive curvature in the Cayley–Klein model are investigated. We conducted their classification, obtained the metric correlations between the measure of angles and the expressions of lengths of the edges through a measure of included angles. 

Key words: 
hyperbolic plane Hˆ with positive curvature
de Sitter plane
parallelogram
parabolic parallelogram
References: 
  1. Romakina L. N. Simple partitions of a hyperbolic plane of positive curvature. Sbornik : Mathematics, 2012, vol. 203, no. 9, pp. 1310–1341. Available at : http://dx.doi.org/10.1070/SM2012v203n09ABEH004266.
  2. Romakina L. N. Veernye trianguliatsii giperbolicheskoi ploskosti polozhitel’noi krivizny [Fan triangulations of hyperbolic plane positive curvature]. Matematicheskie trudy, 2013, vol. 16, no. 2, pp. 142–168 (in Russian).
  3. Romakina L. N. Geometriia giperbolicheskoi ploskosti polozhitel’noi krivizny : v 4 ch. Ch. 2 : Preobrazovaniia i prostye razbieniia [Geometry of the hyperbolic plane of positive curvature : in 4 pt. Pt. 2 : Transformations and simple splittings]. Saratov, Saratov Univ. Press, 274 p. (in Russian).
  4. De Sitter W. On the Relativity of Inertia. Remarks Concerning Einstein’s Latest Hypothesis. Proc. Royal Acad. Amsterdam, 1917, vol. 19, iss. 2, pp. 1217–1225.
  5. Akutagawa K. On space-like hypersurfaces with constant mean curvature in the de Sitter space. Math. Z., 1987, vol. 196, pp. 13–19.
  6. Montiel S. An integral inequality for compact spacelike hypersurfaces in a de Sitter space and application to the case of constant mean curvature. Indiana Univ. Math. J., 1988, vol. 37, pp. 909–917.
  7. Cho Yun. Trigonometry in extended hyperbolic space and extended de Sitter space. Bull. Korean Math. Soc., 2009, vol. 46, no. 6, pp. 1099–1133. DOI : 10.4134/BKMS.2009.46.6.1099.
  8. Asmus Im. Duality between hyperbolic and de Sitter geometry. J. of Geometry, 2009, vol. 96, iss. 1–2, pp. 11–40.
  9. Romakina L. N. Hyperbolic parallelograms of the plane b H. Izv. Sarat. Univ. (N. S.), Ser. Math. Mech. Inform., 2013, vol. 13, iss. 3, pp. 45–52 (in Russian).
  10. Romakina L. N. Analogs of a formula of Lobachevsky for angle of parallelism on the hyperbolic plane of positive curvature. Siberian Electronic Mathematical Reports, 2013, vol. 10, pp. 393–407 (in Russian). Available at: http ://semr.math.nsc.ru
  11. Romakina L. N. Geometriia giperbolicheskoi ploskosti polozhitel’noi krivizny : v 4 ch. Ch. 1 : Trigonometriia [Geometry of the hyperbolic plane of positive curvature : in 4 pt. Pt. 1 : Trigonometry]. Saratov, Saratov Univ. Press., 244 p. (in ussian).
  12. Efimov N. V. Vysshaia geometriia [The highest geometry]. Moscow, Nauka, 1971, 576 p. (in Russian).
Received: 
15.09.2013
Accepted: 
05.01.2014
Published: 
28.02.2014
Short text (in English):
download
(downloads: 193)
  • 1191 reads