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On weakly symmetric generalized Trans-Sasakian manifold

Lovejoy S. Das — 2015

Commentationes Mathematicae

In this paper, we have defined the weakly symmetric generalized Trans-Sasakian manifold $G {(W S)}_{n}$ and it has been shown that on such manifold if any two of the vector field $λ, γ, τ$ defined by equation $A (X) = g (X, λ), B (X) = g (X, μ), C (X) = g (X, γ), D (X) = g (X, τ)$ are orthogonal to $ξ$ , then the third will also be orthogonal to $ξ$ . We have also proved that the scalar curvature $r$ of weakly symmetric generalized Trans-Sasakian manifold $G {(W S)}_{n}$ , $(n > 2)$ satisfies the equation $r = 2 n (α^{2} - β^{2})$ , where $α$ and $β$ are smooth function and $γ \neq τ$ .

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On weakly symmetric generalized Trans-Sasakian manifold

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