Geodesic
On the General Theory of Differentiable Manifolds with Almost Tangent Structure
Canadian mathematical bulletin, Tome 8 (1965) no. 6, pp. 721-748

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Some of the most important G-Structures of the first kind [1] are those defined by linear operators satisfying algebraic relations. If the linear operator J acting on the complexified space of a differentiable manifold V satisfies a relation of the form where I is the identity operator, the manifold has an almost complex structure ([2] [3]). The structures defined by are the almost product structures ([3] [4]). 
Eliopoulos, Hermes A. On the General Theory of Differentiable Manifolds with Almost Tangent Structure. Canadian mathematical bulletin, Tome 8 (1965) no. 6, pp. 721-748. doi: 10.4153/CMB-1965-054-5
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