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 2: The intersection of two of the three groups GL(n, C), O(2n), Sp(2n, R) is equal to the intersection of all the three, and coincides with U(n).

G-structures

Chern, The geometry of G-structures

Sternberg, Lectures on differential geometry (Chap. 7)

Molino, Theorie de G-structures: le probleme d'equivalence

Molino, Sur quelques propriétés des G-structures, J. Diff. Geom. Volume 7, Number 3-4 (1972), 489-518

Kobayashi, Transformation groups in differential geometry

Joyce, Compact manifolds with special holonomy (Chap 2.6)

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