Affiliation:
1. Department of Mathematics, ”Gh. Asachi” Technical University of Iaşi, Iaşi, România
2. ”St. Cyril and St. Methodius” University of Veliko Tarnovo, Faculty of Mathematics and Informatics, Department of Algebra and Geometry, Veliko Tarnovo, Bulgaria
Abstract
This study is devoted to a submanifold M of codimension 2 of an almost
paracontact metric manifold M, for which the Reeb vector field of the
ambient manifold is normal. Some sufficient conditions for the existence of
M are given. When 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 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 M is of a constant
sectional curvature is analysed and an example is constructed.
Publisher
National Library of Serbia
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