Geodesic
The holomorphic conformal submersions Kählerian–Einstein manifolds
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2004) no. 2, pp. 189-207 
S. I. Okrut. The holomorphic conformal submersions Kählerian–Einstein manifolds. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2004) no. 2, pp. 189-207. http://geodesic.mathdoc.fr/item/JMAG_2004_11_2_a5/
@article{JMAG_2004_11_2_a5,
     author = {S. I. Okrut},
     title = {The holomorphic conformal submersions {K\"ahlerian{\textendash}Einstein} manifolds},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {189--207},
     year = {2004},
     volume = {11},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2004_11_2_a5/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In article is given the description of manifolds of Kählerian–Einstein admitting holomorphic conformal submersion with totally geodesic fibers at some additional assumptions on characteristics submersion. It is shown that local obstructions of construction of such metrics are not present. However for complete metrics with compact one-dimensional fibers a diversity is reduced almost that to direct products.