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 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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},
     year = {2015},
     volume = {40},
     number = {1},
     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/