Gray, Alfred; Hervella, Luis M. The sixteen classes of almost Hermitian manifolds and their linear invariants. (English) Zbl 0444.53032 Ann. Mat. Pura Appl., IV. Ser. 123, 35-58 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 63 ReviewsCited in 356 Documents MSC: 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C55 Global differential geometry of Hermitian and Kählerian manifolds 53B35 Local differential geometry of Hermitian and Kählerian structures Keywords:unitary group; almost hermitian manifold; Kaehler form; almost symplectic manifold × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Avez, A.; Lichnerowicz, A.; Diaz-Miranda, A., Sur l’algèbre des automorphismes infinitésimaux d’une variété symplectique, J. Differential Geometry, 9, 1-40 (1974) · Zbl 0283.53033 [2] Berger, M.; Gauduchon, P.; Mazet, E., Le spectre d’une variété riemannienne, Lecture Notes in Mathematics, vol. 194 (1971), Berlin and New York: Springer-Verlag, Berlin and New York · Zbl 0223.53034 [3] Dombrowski, P., On the geometry of the tangent bundle, J. Reine Angew. Math., 210, 73-88 (1962) · Zbl 0105.16002 [4] Donnelly, H., Invariance theory of Hermitian manifolds, Proc. Amer. Math. Soc., 58, 229-233 (1976) · Zbl 0344.53043 [5] Ehresmann, C.; Libermann, P., Sur les formes différentielles extérieures de degré2, C. R. Acad. Sci. Paris, 227, 420-421 (1948) · Zbl 0034.19903 [6] Ehresmann, C.; Libermann, P., Le problème d’équivalence des formes extérieures quadratiques, C. R. Acad. Sci. Paris, 229, 697-698 (1949) · Zbl 0034.20001 [7] Fernández, M.; Hervella, L. M., Un exemple de variété pseudokählérienne, C. R. Acad. Sci. Paris, 283, 203-205 (1976) · Zbl 0342.53034 [8] Gilkey, P., Spectral geometry and the Kähler condition for complex manifolds, Invent. Math., 26, 231-258 (1974) · Zbl 0303.53057 [9] Gray, A., Minimal varieties and almost Hermitian submanifolds, Michigan Math. J., 12, 273-279 (1965) · Zbl 0132.16702 [10] Gray, A., Some examples of almost Hermitian manifolds, Illinois J. Math., 10, 353-366 (1969) · Zbl 0183.50803 [11] Gray, A., Vector cross products on manifolds, Trans. Amer. Math. Soc., 141, 465-504 (1969) · Zbl 0182.24603 [12] Gray, A., Riemannian manifolds with geodesic symmetries of order 3, J. Differential Geometry, 7, 343-369 (1972) · Zbl 0275.53026 [13] Gray, A., The volume of a small geodesic ball in a Riemannian manifold, Michigan Math. J., 20, 329-344 (1973) · Zbl 0279.58003 [14] Gray, A., The structure of nearly Kähler manifolds, Math. Ann., 223, 233-248 (1976) · Zbl 0345.53019 [15] Gray, A., Curvature identities for Hermitian and almost Hermitian manifolds, Tôhoku Math. J., 28, 601-612 (1976) · Zbl 0351.53040 [16] Hervella, L. M.; Vidal, E., Nouvelles géométries pseudo-kählériennes G_1et G_2, C. R. Acad. Sci. Paris, 283, 115-118 (1976) · Zbl 0331.53026 [17] L. M.Hervella - E.Vidal,New pseudo-Kähler geometries, to appear. · Zbl 0331.53026 [18] Iwahori, N., Some remarks on tensor invariants of O(n), U(n), Sp(n), J. Math. Soc. Japan, 10, 145-160 (1958) · Zbl 0082.15601 [19] Kodaira, K.; Morrow, J., Complex Manifolds (1971), New York: Holt, Rinehart and Winston, New York · Zbl 0325.32001 [20] Kotō, S., Some theorems on almost Kählerian spaces, J. Math. Soc. Japan, 12, 422-433 (1960) · Zbl 0192.28303 [21] Lee, H. C., A kind of even-dimensional differential geometry and its application to exterior calculus, Amer. J. Math., 65, 433-438 (1943) · Zbl 0060.38302 [22] T.Lepage,Sur certaines congruences de formes alternées, Bull. Sci. Roy. Soc. Liège (1946), pp. 21-31. · Zbl 0060.04202 [23] Libermann, P., Sur le problème d’équivalence, Thèse, Strasbourg 1953, Ann. Mat. Pura Appl., 36, 27-120 (1954) · Zbl 0056.15401 [24] P.Libermann,Sur la classification des structures hermitiennes, to appear. · Zbl 0443.53031 [25] G.Papy,Sur le divisibilité des formes alternées, Bull. Soc. Roy. Sci. Liège (1946), p. 24. · Zbl 0061.02008 [26] Thurston, W. P., Some examples of symplectic manifolds, Proc. Amer. Math. Soc., 55, 467-468 (1976) · Zbl 0324.53031 [27] Vaisman, I., On locally conformal almost Kähler manifolds, Israel J. Math., 24, 338-351 (1976) · Zbl 0335.53055 [28] E.Vidal Abascal,Algunos resultados sobre variedades casihermiticas, Actas del V congresso de la agrupación de matematicos de expression latina, Palma, 1978. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.