Cycles on the Hyperbolic Plane of Positive Curvature

Abstract

We study properties of hyperbolic and elliptic cycles of a hyperbolic plane Ĥ of positive curvature. An analog of the Pythagorean theorem for a right triangle with a parabolic hypotenuse is proved. For each type of lines, we obtain formulas expressing the length of a chord of a hyperbolic cycle in terms of the radius of the cycle, the measure of the central angle corresponding to the chord, and the radius of curvature of Ĥ. The plane Ĥ is considered in the projective interpretation. Bibliography: 11 titles.