Abstract
In the present paper, we study three-dimensional trans-Sasakian manifolds admitting the Schouten-van Kampen connection. Also, we have proved some results on $\phi$-projectively flat, $\xi-$projectively flat and $\xi-$concircularly flat three-dimensional trans-Sasakian manifold with respect to the Schouten-van Kampen connection. Locally $\phi-$symmetry trans-Sasakian manifolds of dimension three have been studied with respect to Schouten-van Kampen connection. Finally, we construct an example of a three-dimensional trans-Sasakian manifold admitting Schouten-van Kampen connection which verifies Theorem 4.1.
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