Geodesic
On a Riemannian Manifold M 2n with an Almost Tangent Structure
Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 759-769

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Professor Eliopoulous studied almost tangent structures on manifolds M2n in [1; 2]. An almost tangent structure F is a field of class C∞ of linear operations on M2n such that at each point x in M2n, Fx maps the complexified tangent space into itself and that Fx is of rank n everywhere and satisfies that F2 = 0. In this note, we consider a (1,1) tensor field . on a Riemannian M2n which satisfies everywhere and is such that the rank of F is n everywhere. Such gives an almost tangent structure F on M2n. 
Houh, C.S. On a Riemannian Manifold M 2n with an Almost Tangent Structure. Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 759-769. doi: 10.4153/CMB-1969-098-1
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     title = {On a {Riemannian} {Manifold} {M} 2n with an {Almost} {Tangent} {Structure}},
     journal = {Canadian mathematical bulletin},
     pages = {759--769},
     year = {1969},
     volume = {12},
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     doi = {10.4153/CMB-1969-098-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-098-1/}
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