Submanifolds of codimension 2 of paracosymplectic manifolds with normal Reeb vector field

Abstract

This study is devoted to a submanifold $M$ of codimension 2 of an almost paracontact metric manifold $\bar {M}$, for which the Reeb vector field of the ambient manifold is normal. Some sufficient conditions for the existence of $M$ are given. When $\bar {M}$ is paracosymplectic, then some necessary and sufficient conditions are established for $M$ to fall in one of the following classes of almost paracontact metric manifolds according to the classification given by S. Zamkovoy and G. Nakova: normal, paracontact metric, para-Sasakian, K-paracontact, quasi-para-Sasakian, respectively. When in addition, $M$ is para-Sasakian and $\bar  {M}$ is paracosymplectic, some characterization results are obtained for $M$ to be totally umbilical, as well as a nonexistence result for $M$ to be totally geodesic is provided. The case when $\bar {M}$ is of a constant sectional curvature is analysed and an example is constructed.