Geodesic
On the Constant Type of Almost Hermitian Manifolds
Matematičeskie zametki, Tome 68 (2000) no. 5, pp. 668-676.

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We suggest a most natural generalization of the notion of constant type for nearly Kählerian manifolds introduced by A. Gray to arbitrary almost Hermitian manifolds. We prove that the class of almost Hermitian manifolds of zero constant type coincides with the class of Hermitian manifolds. We show that the class of $G_1$-manifolds of zero constant type coincides with the class of 6-dimensional $G_1$-manifolds with a non-integrable structure. Finally, we prove that the class of normal $G_2$-manifolds of nonzero constant type coincides with the class of 4-dimensional $G_2$-manifolds with a nonintegrable structure. 
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V. F. Kirichenko; I. V. Tret'yakova. On the Constant Type of Almost Hermitian Manifolds. Matematičeskie zametki, Tome 68 (2000) no. 5, pp. 668-676. http://geodesic.mathdoc.fr/item/MZM_2000_68_5_a3/

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

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

[3] Vanhecke L., “Constant type for almost Hermitian manifolds”, Bull. Math. Soc. Sci. Math. RSR, 20:3–4 (1976–77), 415–422 | MR | Zbl

[4] Kirichenko V. F., “Pochti ermitovy mnogoobraziya postoyannogo tipa”, Dokl. AN SSSR, 259:6 (1981), 1293–1297 | MR | Zbl

[5] Likhnerovich A., Teoriya svyaznostei v tselom i gruppy golonomii, IL, M., 1960

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

[7] Gray A., Hervella L. M., “The sixteen classes of almost Hermitian manifolds and their linear invariants”, Ann. Math. Pure Appl., 123:4 (1980), 35–58 | DOI | Zbl

[8] Kirichenko V. F., “Metody obobschennoi ermitovoi geometrii v teorii pochti kontaktnykh mnogoobrazii”, Itogi nauki i tekhn. Problemy geometrii, 18, VINITI, M., 1986, 25–71 | MR

[9] 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

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

[12] Blair D. E., “Contact manifolds in Riemannian geometry”, Lecture Notes in Math., 509, 1976, 1–146 | MR