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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 τ .

On weakly symmetric generalized trans-sasakian manifold

Levejoy S. DasRam NivasRupali Agnihotri — 2014

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 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 ( W S ) n , ( n > 2 ) satisfies the equation r = 2 n ( α 2 β 2 ) , where α and β are smooth function and γ τ .

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