Geodesic
L\"obell manifolds revised
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 605-609

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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. 
@article{SEMR_2007_4_a32,
     author = {A. D. Mednykh and A. Yu. Vesnin},
     title = {L\"obell manifolds revised},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {605--609},
     publisher = {mathdoc},
     volume = {4},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2007_4_a32/}
}
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A. D. Mednykh; A. Yu. Vesnin. L\"obell manifolds revised. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 605-609. http://geodesic.mathdoc.fr/item/SEMR_2007_4_a32/