  A structure on an almost contact metric manifold is defined as a
generalization of well-known cases: Sasakian, quasi-Sasakian, Kenmotsu and
cosymplectic. Then we consider a semi-invariant $\xi^{\bot}$-submanifold of a
manifold endowed with such a structure and two topics are studied: the
integrability of distributions defined by this submanifold and
characterizations for the totally umbilical case. In particular we recover
results of Kenmotsu, Eum and Papaghiuc.
