Summary
It is shown that in a natural way there are precisely sixteen classes of almost Hermitian manifolds.
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A. Avez -A. Lichnerowicz -A. Diaz-Miranda,Sur l'algèbre des automorphismes infinitésimaux d'une variété symplectique, J. Differential Geometry,9 (1974), pp. 1–40.
M. Berger -P. Gauduchon -E. Mazet,Le spectre d'une variété riemannienne, Lecture Notes in Mathematics, vol. 194, Springer-Verlag, Berlin and New York, 1971.
P. Dombrowski,On the geometry of the tangent bundle, J. Reine Angew. Math.,210 (1962), pp. 73–88.
H. Donnelly,Invariance theory of Hermitian manifolds, Proc. Amer. Math. Soc.,58 (1976), pp. 229–233.
C. Ehresmann -P. Libermann,Sur les formes différentielles extérieures de degré 2, C. R. Acad. Sci. Paris,227 (1948), pp. 420–421.
C. Ehresmann -P. Libermann,Le problème d'équivalence des formes extérieures quadratiques, C. R. Acad. Sci. Paris,229 (1949), pp. 697–698.
M. Fernández -L. M. Hervella,Un exemple de variété pseudokählérienne, C. R. Acad. Sci. Paris, 283 (1976), pp. 203–205.
P. Gilkey,Spectral geometry and the Kähler condition for complex manifolds, Invent. Math.,26 (1974), pp. 231–258.
A. Gray,Minimal varieties and almost Hermitian submanifolds, Michigan Math. J.,12 (1965), pp. 273–279.
A. Gray,Some examples of almost Hermitian manifolds, Illinois J. Math.,10 (1969), pp. 353–366.
A. Gray,Vector cross products on manifolds, Trans. Amer. Math. Soc.,141 (1969), pp. 465–504.
A. Gray,Riemannian manifolds with geodesic symmetries of order 3, J. Differential Geometry,7 (1972), pp. 343–369.
A. Gray,The volume of a small geodesic ball in a Riemannian manifold, Michigan Math. J.,20 (1973), pp. 329–344.
A. Gray,The structure of nearly Kähler manifolds, Math. Ann.,223 (1976), pp. 233–248.
A. Gray,Curvature identities for Hermitian and almost Hermitian manifolds, Tôhoku Math. J.,28 (1976), pp. 601–612.
L. M. Hervella -E. Vidal,Nouvelles géométries pseudo-kählériennes G1 et G2, C. R. Acad. Sci. Paris,283 (1976), pp. 115–118.
L. M.Hervella - E.Vidal,New pseudo-Kähler geometries, to appear.
N. Iwahori,Some remarks on tensor invariants of O(n), U(n), Sp(n), J. Math. Soc. Japan,10 (1958), pp. 145–160.
K. Kodaira -J. Morrow,Complex Manifolds, Holt, Rinehart and Winston, New York, 1971.
S. Kotō,Some theorems on almost Kählerian spaces, J. Math. Soc. Japan,12 (1960), pp. 422–433.
H. C. Lee,A kind of even-dimensional differential geometry and its application to exterior calculus, Amer. J. Math.,65 (1943), pp. 433–438.
T.Lepage,Sur certaines congruences de formes alternées, Bull. Sci. Roy. Soc. Liège (1946), pp. 21–31.
P. Libermann,Sur le problème d'équivalence, Thèse, Strasbourg 1953, Ann. Mat. Pura Appl.,36 (1954), pp. 27–120.
P.Libermann,Sur la classification des structures hermitiennes, to appear.
G.Papy,Sur le divisibilité des formes alternées, Bull. Soc. Roy. Sci. Liège (1946), p. 24.
W. P. Thurston,Some examples of symplectic manifolds, Proc. Amer. Math. Soc.,55 (1976), pp. 467–468.
I. Vaisman,On locally conformal almost Kähler manifolds, Israel J. Math.,24 (1976) pp. 338–351.
E.Vidal Abascal,Algunos resultados sobre variedades casihermiticas, Actas del V congresso de la agrupación de matematicos de expression latina, Palma, 1978.
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Gray, A., Hervella, L.M. The sixteen classes of almost Hermitian manifolds and their linear invariants. Annali di Matematica pura ed applicata 123, 35–58 (1980). https://doi.org/10.1007/BF01796539
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DOI: https://doi.org/10.1007/BF01796539