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The purpose of this paper is to study the principal fibre bundle (P, M, G, π p ) with Lie group G, where M admits Lorentzian almost paracontact structure (Ø, ξ p , η p , g) satisfying certain condtions on (1, 1) tensor field J, indeed possesses an almost product structure on the principal fibre bundle. In the later sections, we have defined trilinear frame bundle and have proved that the trilinear frame bundle is the principal bundle and have proved in Theorem 5.1 that the Jacobian map π * is the isomorphism.

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→ D b be the projection map defined by π b ( x a : a ∈ α ) = x b . Conversely, let ι a : D a → D be the embedding defined by ι a ( y ) = ( x b : b ∈ α ), where x a = y and x b = 0 for b ≠ a . Suppose x ∈ N r n D \ {0

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