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تسجيل مستخدم جديدOn $3$-dimensional $left(varepsilon right)$-para Sasakian manifold
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Punam Gupta
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The purpose of the present paper is to study the globally and locally $varphi $-${cal T}$-symmetric $left( varepsilon right) $-para Sasakian manifold in dimension $3$. The globally $varphi $-$ {cal T}$-symmetric $3$-dimensional $left( varepsilon right) $-para Sasakian manifold is either Einstein manifold or has a constant scalar curvature. The necessary and sufficient condition for Einstein manifold to be globally $varphi $-${cal T}$ -symmetric is given. A $3$-dimensional $% left( varepsilon right) $ -para Sasakian manifold is locally $varphi $-$ {cal T}$-symmetric if and only if the scalar curvature $r$ is constant. A $3 $-dimensional $left( varepsilon right) $-para Sasakian manifold with $% eta $-parallel Ricci tensor is locally $varphi $-${cal T}$-symmetric. In the last, an example of $3$-dimensional locally $varphi $-${cal T}$-symmetric $left( varepsilon right) $-para Sasakian manifold is given.
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