Some Properties of \(\epsilon\)-Kenmotsu Manifolds With Quarter-Symmetric Non-Metric Connection

The objective of this paper is to investigate the \(\epsilon\)-Kenmotsu manifolds with quartersymmetric non-metric connection. We have investigate an \(\epsilon\)-Kenmotsu manifolds admitting the quarter-symmetric non-metric connections satisfying certain conditions. We have further provided the equivalent conditions for Ricci soliton in an \(\epsilon\)-Kenmotsu manifolds to be shrinking or expanding with the quarter-symmetric non-metric connection. We have also investigated \(\phi\)-projectively flat, Quasiprojectively flat and some interesting results. Finally, we have given an example of 3-dimensional \(\epsilon\)-Kenmotsu manifolds with respect to quarter-symmetric non-metric connection.