Geodesic
Cycles of the hyperbolic plane of positive curvature
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 12, Tome 415 (2013), pp. 137-162 Cet article a éte moissonné depuis la source Math-Net.Ru

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Properties of hyperbolic and elliptic cycles of the hyperbolic plane $\widehat H$ of positive curvature are investigated. An analog of Pythagorean theorem for a right trivertex with a parabolic hypotenuse is proved. For each type of straight lines, formulas expressing the length of a chord of a hyperbolic cycle in terms of the cycle radius, the measure of the central angle corresponding to the chord, and the radius of curvature of $\widehat H$ are obtained. The plane $\widehat H$ is considered in projective interpretation. 
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L. N. Romakina. Cycles of the hyperbolic plane of positive curvature. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 12, Tome 415 (2013), pp. 137-162. http://geodesic.mathdoc.fr/item/ZNSL_2013_415_a14/

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