A negative transverse first Chern class implies a unique transverse Kähler-Einstein metric on homologically orientable transversally Kähler foliations.
Aubin, ´Equations du type Monge-Amp` ere sur les vari´ et´ es Riemanni- ennes compactes, C.R
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An Aubin-Yau theorem for transversally K\"ahler foliations
A negative transverse first Chern class implies a unique transverse Kähler-Einstein metric on homologically orientable transversally Kähler foliations.