Let be an almost contact metric manifold. is a Kenmotsu manifold if
[K. Kenmotsu, Tôhoku Math. J. 24, 93-103 (1972; Zbl 0245.53040)]. An immersed submanifold of is called anti-invariant if forall .
The author establishes several properties of the geometric objects on such a manifold , when the vector field is tangent to and when is normal to .