Geodesic
Killing $f$-manifolds of constant type
Izvestiya. Mathematics , Tome 63 (1999) no. 5, pp. 963-981

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The notion of constancy of type was introduced by Gray in the study of specific properties of the geometry of six-dimensional nearly Kahlerian manifolds, and has been investigated by many authors. This notion can be generalized in a natural manner to the case of metric $f$-manifolds with the Killing fundamental form (Killing $f$-manifolds). In this paper, the property of constancy of type is studied in the naturally arising class of so-called commutatively Killing $f$-manifolds, and some of their remarkable properties are investigated. An exhaustive description of commutatively Killing $f$-manifolds of constant type is obtained. In particular, it is proved that the constancy of type of commutatively Killing $f$-manifolds is tantamount to their local equivalence to the five-dimensional sphere $S^5$ endowed with the weakly cosymplectic structure induced by a special embedding of $S^5$ in the Cayley numbers. 
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     author = {V. F. Kirichenko and L. V. Lipagina},
     title = {Killing $f$-manifolds of constant type},
     journal = {Izvestiya. Mathematics },
     pages = {963--981},
     publisher = {mathdoc},
     volume = {63},
     number = {5},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1999_63_5_a3/}
}
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V. F. Kirichenko; L. V. Lipagina. Killing $f$-manifolds of constant type. Izvestiya. Mathematics , Tome 63 (1999) no. 5, pp. 963-981. http://geodesic.mathdoc.fr/item/IM2_1999_63_5_a3/