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Journal for Geometry and Graphics 22 (2018), No. 1, 067--086
Copyright Heldermann Verlag 2018

To the Volumes Theory of a Hyperbolic Space of Positive Curvature

Lyudmila Romakina
Dept. of Geometry, Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia

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.

Keywords: Cayley-Klein model, hyperbolic space of positive curvature, volume, monopolar tetrahedron.

MSC: 51F10; 14Q10, 51M25

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