L\"obell manifolds revised

A. D. Mednykh ; A. Yu. Vesnin

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 605-609.

Résumé

The first example of a closed orientable hyperbolic $3$-manifold was constructed by F. Löbell in 1931. It was an affirmative answer to the Köbe question on the existence of hyperbolic $3$-forms. In the present paper we give a short survey of some related results and obtain a simple analytic formula for the volume of the Löbell manifold as well as for volumes of Humbert manifolds.

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