Geometry of spaces of constant curvature. (Russian) Zbl 0699.53001
Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 29, 5-146 (1988).
[For the entire collection see Zbl 0643.00020.]
The basic results of the geometry of spaces of constant curvature are presented, with special emphasis on the Lobatschevsky space. In addition the spaces of constant curvature are defined as homogeneous spaces of maximal mobility. Such axiomatic approach allows to pass freely from one model of a space of constant curvature to the other and a quick access to analytical instruments. In the last part of the paper spaces of constant curvature are considered as Riemannian manifolds.
The basic results of the geometry of spaces of constant curvature are presented, with special emphasis on the Lobatschevsky space. In addition the spaces of constant curvature are defined as homogeneous spaces of maximal mobility. Such axiomatic approach allows to pass freely from one model of a space of constant curvature to the other and a quick access to analytical instruments. In the last part of the paper spaces of constant curvature are considered as Riemannian manifolds.
Reviewer: A.Fleischer
MSC:
| 53-02 | Research exposition (monographs, survey articles) pertaining to differential geometry |
| 53C20 | Global Riemannian geometry, including pinching |
| 51M05 | Euclidean geometries (general) and generalizations |
| 53C30 | Differential geometry of homogeneous manifolds |
| 51M10 | Hyperbolic and elliptic geometries (general) and generalizations |
