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Keywords:
Trans-Sasakian manifold; $\xi $-projectively flat; $\phi $-projectively flat; Einstein manifold
Trans-Sasakian manifold; $\xi $-projectively flat; $\phi $-projectively flat; Einstein manifold
Summary:
The object of the present paper is to study $\xi $-projectively flat and $\phi $-projectively flat 3-dimensional connected trans-Sasakian manifolds. Also we study the geometric properties of connected trans-Sasakian manifolds when it is projectively semi-symmetric. Finally, we give some examples of a 3-dimensional trans-Sasakian manifold which verifies our result.
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