Erken, İrem Küpeli2021-03-202021-03-2020201422-63831420-9012http://doi.org/10.1007/s00025-020-01217-0https://hdl.handle.net/20.500.12885/410The principal objective of this paper is to answer positively the open question whether every invariant submanifold of a paracontact metric ((kappa) over tilde, (mu) over tilde)-manifold is totally geodesic. Main result is that any invariant submanifold of a paracontact metric ((kappa) over tilde, (mu) over tilde)-manifold, (kappa) over tilde not equal -1, is always totally geodesic. Additionally, if (kappa) over tilde not equal - 1 and (mu) over tilde not equal 0 the result can be partially reversed, which shows that the totally geodesic submanifold is invariant under the flow of characteristic vector field is tangent to the submanifold.eninfo:eu-repo/semantics/closedAccessParacontact metric manifoldinvariant submanifolds(kappa, mu)-manifoldArticle10.1007/s00025-020-01217-0753WOS:000542647000002Q2Q2