ON THREE-DIMENSIONAL TRANS-SASAKIAN MANIFOLDS ADMITTING SCHOUTEN-VAN KAMPEN CONNECTION

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.