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Note on Almost Product Manifolds and their Tangent Bundles
Published online by Cambridge University Press: 20 November 2018
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Let Mn be an n-dimensional manifold of differentiability class C∞ with an almost product structure 
. Let 
have eigenvalue +1 of multiplicity p and eigenvalue -1 of multiplicity q where p+q = n and p≧1, q≧1. Let T(Mn) be the tangent bundle of M. T(Mn) is a 2n dimensional manifold of class C∞. Let xi be the local coordinates of a point P of Mn. The local coordinates of T(Mn) can be expressed by 2n variables (xi, yi) where xi are coordinates of the point P and yi are components of a tangent vector at P with respect to the natural frame constituted by the vectior ∂/∂xi at P.
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- Copyright © Canadian Mathematical Society 1966
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