Geodesic
Singular Riemannian Structures Compatible with π-Structures
Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 705-719

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G. Legrand [1] studied a generalization of the almost complex structures [2] by considering a linear operator J acting on the complexified space of a differentiable manifold Vm satisfying a relation of the form J2 = λ2 (identity) where λ is a nonzero complex constant. Such structures are called π-structures. A π-structure is defined on Vm by the knowledge of two fields, of proper supplementary subspaces T1 and T2 of the complexified tangent space at x ∈ Vm, such that dim(T1) = n1; dim(T2) = n2; n1 + n2 = m. In the remaining case, λ= 0, H. A. Eliopoulos [3] introduced almost tangent structures and discussed euclidean structures compatible with almost tangent structures [4]. In a similar way the purpose of this paper is to study singular riemannian structures compatible with π structures, briefly Rπ-structures. 
Duggal, K. L. Singular Riemannian Structures Compatible with π-Structures. Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 705-719. doi: 10.4153/CMB-1969-092-8
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