Geodesic
Codimension 2 submanifolds of paracosymplectic manifolds with normal Reeb vector field
Filomat, Tome 37 (2023) no. 25, p. 8693

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DOI

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.
DOI : 10.2298/FIL2325693B
Classification : 53C15, 53C40, 53C25
Keywords: Submanifold, Almost paracontact metric manifold, Paracosymplectic manifold, Para-Sasakian manifold 
Cornelia-Livia Bejan; Galia Nakova. Codimension 2 submanifolds of paracosymplectic manifolds with normal Reeb vector field. Filomat, Tome 37 (2023) no. 25, p. 8693 . doi: 10.2298/FIL2325693B
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     author = {Cornelia-Livia Bejan and Galia Nakova},
     title = {Codimension 2 submanifolds of paracosymplectic manifolds with normal {Reeb} vector field},
     journal = {Filomat},
     pages = {8693 },
     year = {2023},
     volume = {37},
     number = {25},
     doi = {10.2298/FIL2325693B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2325693B/}
}
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