Geodesic
To the Volumes Theory of a Hyperbolic Space of Positive Curvature
Journal for geometry and graphics, Tome 22 (2018) no. 1, pp. 67-86.

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In the Cayley-Klein model a hyperbolic space H3 of positive curvature is realized on the ideal domain of the Lobachevskii space, that is, on the exterior domain of the projective space P3 with respect to an oval surface. In this paper the basic notions of the volumes theory of the space H3 are introduced through projective invariants of the fundamental group of this space. The volume formulae for a monopolar tetrahedron and bodies bounded by a hypersphere of the space H3 are obtained.
Classification : 51F10, 14Q10, 51M25
Mots-clés : Cayley-Klein model, hyperbolic space of positive curvature, volume, monopolar tetrahedron 
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     title = {To the {Volumes} {Theory} of a {Hyperbolic} {Space} of {Positive} {Curvature}},
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L. Romakina . To the Volumes Theory of a Hyperbolic Space of Positive Curvature. Journal for geometry and graphics, Tome 22 (2018) no. 1, pp. 67-86. http://geodesic.mathdoc.fr/item/JGG_2018_22_1_JGG_2018_22_1_a7/