EUDML

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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Second order parallel tensors on $α$ – Sasakian manifold.

Submanifolds of $F$ -structure manifold satisfying $F^{K} + {(-)}^{K + 1} F = 0$ .

Submanifolds of $F$ -structure manifold satisfying $F^{K} + {(-)}^{(K + 1)} F = 0$ .

Complete lift of a structure satisfying $f^{k} - {(- 1)}^{k + 1} f = 0$ .

On a structure satisfying $F^{k} - {(- 1)}^{k + 1} F = 0$ .

Prolongations of $F$ -structure to the tangent bundle of order 2.

On horizontal and complete lifts from a manifold with $f_{λ} (7, 1)$ -structure to its cotangent bundle.

On submanifolds of codimension 2 immersed in a Hsu--quarternion manifold.

On weakly symmetric generalized Trans-Sasakian manifold