Geodesic
On a Class of Almost-Hermitian Structures on Tangent Bundles
Matematičeskie zametki, Tome 76 (2004) no. 5, pp. 732-739.

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We construct a new almost-Hermitian structure of anti-invariant type on tangent bundles and deduce criteria for this structure to belong to all the Gray–Hervella classes. In particular, we prove that the tangent bundles over Kählerian and semi-Kählerian manifolds carry, respectively, a Kählerian and a semi-Kählerian structure. 
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B. V. Zayatuev. On a Class of Almost-Hermitian Structures on Tangent Bundles. Matematičeskie zametki, Tome 76 (2004) no. 5, pp. 732-739. http://geodesic.mathdoc.fr/item/MZM_2004_76_5_a8/

[1] Dombrovski P., “On the geometry of the tangent bundles”, J. Reine Angew. Math., 210 (1962), 73–88 | MR

[2] Tachibana Shun-ichi, Okumura M., “On the almost-complex structure of tangent bundles of Riemannian spaces”, Tôhoku Math. J. (2), 14 (1962), 156–161 | DOI | MR | Zbl

[3] Kirichenko V. F., Zayatuev B. V., “Differentsialnaya geometriya tangentsialnykh ermitovykh poverkhnostei”, UMN, 51:3 (1996), 203–204 | MR | Zbl

[4] Tahare M., Watanabe V., “Natural almost Hermition, Hermition and Kaehlerian metrics on the tangent bundles”, Math. J. Toyama Univ., 20 (1997), 35–41

[5] Papaghiuc N., “The new example Kaehlerian structure on the tangent bundele of space form”, Demonstr. Math., 31:4 (1998), 81–87 | MR

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

[7] Kirichenko V. F., “$K$-prostranstva postoyannoi golomomorfnoi sektsionnoi krivizny”, Matem. zametki, 19:5 (1976), 805–814 | MR | Zbl

[8] Yano K., Ishihara S., Tangent and Cotangent Bundles, Marcel Dekker, New York, 1973 | Zbl

[9] Zayatuev B. V., “On geometry of tangent Hermition surfaces”, Webs and Quasigroups. T.S.U., 1995, 139–143 | MR

[10] Zayatuev B. V., “O nekotorykh klassakh $AH$-struktur na kasatelnom rassloenii”, Trudy mezhdunarodnoi konferentsii, posvyaschennoi A. Z. Petrovu, 2000, 53–54

[11] Zayatuev B. V., “About some classes of almost Hermition structure on tangent bundele”, Webs and Quasigroups. T.S.U., 2002, 103–106 | MR

[12] Nakayama S., “Conformal relations in almost Hermitian spaces”, Tensor, 12:3 (1962), 278–289 | MR | Zbl

[13] Hervella L. M., Vidal E., “Nouvelles geometries pseudo-kahleriennes $G_1$ et $G_2$”, C. R. Acad. Sci. Paris, 283 (1976), 115–118 | MR | Zbl

[14] Gray A., “The structure of nearly Kaehler manifolds”, Ann. Math., 223:3 (1976), 233–248 | DOI | MR | Zbl

[15] Kirichenko V. F., “Differentsialnaya geometriya K-prostranstv”, Itogi nauki i tekhniki. Problemy geometrii, 8, VINITI AN SSSR, M., 1977, 139–161

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

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

[18] Apte M., “Sur certaines varietes hermetiques”, C. R. Acad. Sci. Paris, 238:19 (1954), 1091–1093 | MR