Geodesic
Bochner-flat Kähler manifolds and Riemannian compatibility of the Ricci tensor
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 40 (2015) no. 1.

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

In this paper we investigate Riemannian compatibility of Ricci tensor of a Bochner-flat Kähler manifold, and specially of a such manifolds which is of quasi-constant holomorphic sectional curvature. Also, we extend our consideration to manifolds without Bochner-flat condition. In all cases we found necessary and sufficient conditions on the Ricci tensor of considered manifolds to be Riemannian compatible. 
@article{BASS_2015_40_1_a1,
     author = {Mileva Prvanovi\'c},
     title = {Bochner-flat {K\"ahler} manifolds and {Riemannian} compatibility of the {Ricci} tensor},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {11 - 18},
     publisher = {mathdoc},
     volume = {40},
     number = {1},
     year = {2015},
     url = {http://geodesic.mathdoc.fr/item/BASS_2015_40_1_a1/}
}
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Mileva Prvanović. Bochner-flat Kähler manifolds and Riemannian compatibility of the Ricci tensor. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 40 (2015) no. 1. http://geodesic.mathdoc.fr/item/BASS_2015_40_1_a1/