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On weakly symmetric generalized trans-sasakian manifold

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Das L. S. , Nivas R. , Agnihotri R.

Commentationes Mathematicae

2014

tom Vol 54, No. 1

141--145

In this paper, we have defined the weakly symmetric generalized Trans-Sasakian manifold G(WS)n and it has been shown that on such manifold if any two of the vector fields λ,γ,τ, defined by equation (0.3) 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(WS)n, (n>2) satisfies the equation r=2n(α2−β2), where α and β are smooth function and γ≠τ.

On weakly symmetric generalized Trans-Sasakian manifold

100%

Das L. S.

Commentationes Mathematicae

2015

tom 55

nr 1

In this paper, we have defined the weakly symmetric generalized Trans-Sasakian manifold \(G(WS)_n\) and it has been shown that on such manifold if any two of the vector field \(\lambda,\gamma,\tau\) defined by equation \[ A(X)=g(X,\lambda), B(X)=g(X,\mu), C(X)=g(X,\gamma), D(X)=g(X,\tau) \] are orthogonal to \(\xi\), then the third will also be orthogonal to \(\xi\). We have also proved that the scalar curvature \(r\) of weakly symmetric generalized Trans-Sasakian manifold \(G(WS)_n\), \((n>2)\) satisfies the equation \(r=2n(\alpha^2-\beta^2)\), where \(\alpha\) and \(\beta\) are smooth function and \(\gamma\neq\tau\).