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Singular Riemannian Structures Compatible with π-Structures

Published online by Cambridge University Press:  20 November 2018

K. L. Duggal
K. L. Duggal*
Affiliation:
University of Windsor, Windsor, Ontario
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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.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 6 , December 1969 , pp. 705 - 719
Copyright
Copyright © Canadian Mathematical Society 1969

References

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