Summary: The objective of the present paper is to study some new results on an \(\varepsilon \)-Kenmotsu manifold with a semi-symmetric metric connection. It is shown that the manifold satisfying the conditions \(\bar {R} \cdot \bar {S} = 0\) and \(\bar {S} \cdot \bar {R} = 0\) is an \(\eta \)-Einstein manifold. Also, we obtain the conditions for the manifold with a semi-symmetric metric connection to be conformally flat.