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On isometries of space forms. (English) Zbl 0789.53027
Szenthe, J. (ed.) et al., Differential geometry and its applications. Proceedings of a colloquium, held in Eger, Hungary, August 20-25, 1989, organized by the János Bolyai Mathematical Society. Amsterdam: North- Holland Publishing Company. Colloq. Math. Soc. János Bolyai. 56, 509-534 (1992).
The paper splits into two parts. The first one deals with a well known candidate for a closed hyperbolic 3-manifold of minimal volume (Weeks- Fomenko-Matveev manifold $$M_ 0$$, $$\text{vol}M_ 0 = 0.94\dots$$) see A. T. Fomenko and S. V. Matveev [Russ. Math. Surv. 43, No. 1, 3-24 (1988); translation from Usp. Mat. Nauk 43, No. 1, 5-22 (1988; Zbl 0671.58008)]. The author shows that $$M_ 0$$ does not regularly cover another closed hyperbolic 3-manifold and its isometry group is a Coxeter group of order 12. The second part studies minimal closed geodesics of closed non-oriented hyperbolic 3-manifolds in some infinite series combinatorically constructed by the author. Arguing to symmetries of corresponding Dirichlet polyhedra, he also describes isometries of these manifolds [see also K. P. Makarova, F. L. Damian and V. V. Balkan, Mat. Issled. 103, 151-163 (1988; Zbl 0669.51012)].
For the entire collection see [Zbl 0764.00002].

##### MSC:
 53C20 Global Riemannian geometry, including pinching 53C22 Geodesics in global differential geometry