Geodesic
Thurston geometries on bases of bundles of homogeneous spaces
Izvestiya. Mathematics , Tome 63 (1999) no. 4, pp. 667-686

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Natural Seifert bundles for plesiocompact (in particular, compact) homogeneous spaces $M$ are considered. Conditions are given for the realizability of compact forms of Thurston geometries of dimension less than or equal to four on the bases $M_a^*$ of these bundles. The structure of these $M_a^*$ is discussed in detail. 
@article{IM2_1999_63_4_a2,
     author = {V. V. Gorbatsevich},
     title = {Thurston geometries on bases of bundles of homogeneous spaces},
     journal = {Izvestiya. Mathematics },
     pages = {667--686},
     publisher = {mathdoc},
     volume = {63},
     number = {4},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1999_63_4_a2/}
}
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V. V. Gorbatsevich. Thurston geometries on bases of bundles of homogeneous spaces. Izvestiya. Mathematics , Tome 63 (1999) no. 4, pp. 667-686. http://geodesic.mathdoc.fr/item/IM2_1999_63_4_a2/