Geodesic
Riemannian Structures Subordinate to Certain Almost Tangent Structures
Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 71-77

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Almost tangent structures have been studied by Eliopoulos [1] and certain Riemannian structures subordinate to almost tangent structures have been studied by Closs [2]. In this paper we investigate those subordinate Riemannian structures for which the underlying almost tangent structure is without torsion and those for which the fundamental form is closed.Similar studies have been carried out with respect to Riemannian structures subordinate to almost complex structures by Lichnerowicz [4] and with respect to Riemannian structures subordinate to almost product structures by Legrand [5]. 
Closs, M. P. Riemannian Structures Subordinate to Certain Almost Tangent Structures. Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 71-77. doi: 10.4153/CMB-1972-014-8
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[1] 1. Eliopoulos, H. A., On the general theory of differentiable manifolds with almost tangent structure, Canad. Math. Bull. (6) 8 (1965), 721-748. Google Scholar

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