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Characterization of Riemannian manifolds with weak holonomy group \(G_2\) (following A. Gray). (English) Zbl 0449.53026


MSC:

53C05 Connections (general theory)
53C10 \(G\)-structures

Citations:

Zbl 0222.53043
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Full Text: DOI EuDML

References:

[1] Borel, A.: Sur l’homologie et la cohomologie des groupes de Lie compacts connexes. Amer. J. Math.76, 273-342 (1954) · Zbl 0056.16401 · doi:10.2307/2372574
[2] Brown, R.B., Gray, A.: Vector cross products. Comment. Math. Helv.42, 222-236 (1967) · Zbl 0155.35702 · doi:10.1007/BF02564418
[3] Gray, A.: Weak holonomy groups. Math. Z.123, 290-300 (1971) · Zbl 0222.53043 · doi:10.1007/BF01109983
[4] Gray, A.: Nearly Kähler manifolds. J. Differential Geometry4, 283-310 (1970) · Zbl 0201.54401
[5] Gray, A.: Vector cross products on manifolds. Trans. Amer. Math. Soc.14, 465-504 (1969) · Zbl 0182.24603 · doi:10.1090/S0002-9947-1969-0243469-5
[6] Jacobson, M.: Composition algebras and their automorphisms. Rend. Circ. Mat. Palermo7, 55-80 (1958) · Zbl 0083.02702 · doi:10.1007/BF02854388
[7] Simons, J.: On transitivity of holonomy systems. Ann. of Math.76, 213-234 (1962) · Zbl 0106.15201 · doi:10.2307/1970273
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