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On weakly symmetric generalized Trans-Sasakian manifold

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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 \(\gamma\neq\tau\).

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1 Commentationes Mathematicae

1 Das L. S.

1 2015

Wyniki wyszukiwania

On weakly symmetric generalized Trans-Sasakian manifold