THE AREA OF A GENERALIZED POLYGON WITHOUT PARABOLIC EDGES OF A HYPERBOLIC PLANE OF POSITIVE CURVATURE

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Published: 2016-01-04

Page: 293-310


LYUDMILA ROMAKINA *

Department of Geometry, Saratov State University, 83 Astrakhanskaya Street, 410012 Saratov, Russia.

*Author to whom correspondence should be addressed.


Abstract

The geometry of a hyperbolic plane Ĥ of positive curvature can be realized on ideal domain of the Lobachevskii plane ∧2. The planes Ĥ and ∧2 are components of an extended hyperbolic plane H2, i.e. the projective plane P2 with the oval curve ϒ fixed on it. In this article the formula of expression of the area of the generalized polygon without parabolyc edges on the plane Ĥ through measures of its internal angles is proved.

Keywords: The hyperbolic plane Ĥ of positive curvature, a generalized polygon of the plane Ĥ, the area of a generalized polygon of the plane Ĥ


How to Cite

ROMAKINA, L. (2016). THE AREA OF A GENERALIZED POLYGON WITHOUT PARABOLIC EDGES OF A HYPERBOLIC PLANE OF POSITIVE CURVATURE. Asian Journal of Mathematics and Computer Research, 10(4), 293–310. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/329

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