Geodesic
$K$-spaces of maximal rank
Matematičeskie zametki, Tome 22 (1977) no. 4, pp. 465-476.

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We consider a special type of $K$-space, i.e., almost-Hermitian manifolds whose fundamental form is a Killing form. The $K$-spaces of this type are characterized by the fact that their dimension is equal to the rank of the covariant derivative of the structure form. A number of the properties of such spaces are established (they are Einstein, compact, have finite fundamental group, etc.). It is proved that every $K$-space is locally equivalent to a product of a $K$-space of maximal rank and a Kähler manifold. The $K$-spaces with zero holomorphic sectional curvature are studied. 
@article{MZM_1977_22_4_a0,
     author = {V. F. Kirichenko},
     title = {$K$-spaces of maximal rank},
     journal = {Matemati\v{c}eskie zametki},
     pages = {465--476},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_4_a0/}
}
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V. F. Kirichenko. $K$-spaces of maximal rank. Matematičeskie zametki, Tome 22 (1977) no. 4, pp. 465-476. http://geodesic.mathdoc.fr/item/MZM_1977_22_4_a0/