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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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/

[1] Gray A., “Nearly Kähler manifolds”, J. Different. Geom., 4:3 (1970), 283–309 | MR | Zbl

[2] Naveira A., Hervella L. M., “Shur's theorem for nearly Kähler manifolds”, Proc. Amer. Math. Soc., 49:2 (1975), 421–425 | DOI | MR | Zbl

[3] Vanhecke L., Bouten F., “Constant type for almost Hermitian manifolds”, Bull. Math. Soc. sci. math. RSR, 20:3–4 (1976–1977), 415–422 | MR | Zbl

[4] Gritsans A. S., “O geometrii killingovykh $f$-mnogoobrazii”, UMN, 45:4 (1990), 149–150 | MR | Zbl

[5] Blair D. E., Showers D. K., “Almost contact manifolds with Killing structure tensors, II”, J. Different. Geom., 9:4 (1974), 577–582 | MR | Zbl

[6] Kirichenko V. F., “$K$-algebry i $K$-prostranstva postoyannogo tipa s indefinitnoi metrikoi”, Matem. zametki, 29:2 (1981), 265–278 | MR | Zbl

[7] Kirichenko V. F., “$K$-prostranstva postoyannogo tipa”, Sib. matem. zhurn., 17:2 (1976), 282–289 | MR | Zbl

[8] Kiritchenko V. F., “Sur le geometrie des varietes approximativement cosymplectiques”, C. r. Acad. Sci., Paris, 295:1 (1982), 673–676 | MR | Zbl

[9] Kirichenko V. F., “Kvaziodnorodnye mnogoobraziya i obobschennye pochti ermitovy struktury”, Izv. AN SSSR. Ser. matem., 47:6 (1983), 1208–1223 | MR | Zbl

[10] Kirichenko V. F., “Generalized quasi-Kaehlerian manifolds and axioms of $CR$-submanifolds in generalized Hermitian geometry, I”, Geometriae Dedicata, 51 (1994), 75–104 | DOI | MR | Zbl

[11] Kirichenko V. F., “Generalized quasi-Kaehlerian manifolds and axioms of $CR$-submanifolds in generalized Hermitian geometry, II”, Geometriae Dedicata, 52 (1994), 53–85 | DOI | MR | Zbl

[12] Kirichenko V. F., “Aksioma $\Phi $-golomorfnykh ploskostei v kontaktnoi metricheskoi geometrii”, Izv. AN SSSR. Ser.matem., 48:4 (1984), 711–734 | MR | Zbl

[13] Kobayashi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, Nauka, M., 1981