Invariant submanifolds of Sasakian manifolds admitting semisymmetric nonmetric connection
Summary: The object of this paper is to study invariant submanifolds \(M\) of Sasakian manifolds \(\widetilde{M}\) admitting a semisymmetric nonmetric connection, and it is shown that \(M\) admits a semisymmetric nonmetric connection. Further it is proved that the second fundamental forms \(\sigma\) and \(\overline{\sigma}\) with respect to the Levi-Civita connection and the semi-symmetric nonmetric connection coincide. It is shown that if the second fundamental form \(\sigma\) is recurrent, 2-recurrent, generalized 2-recurrent, semiparallel, pseudoparallel, and Ricci-generalized pseudoparallel and \(M\) has parallel third fundamental form with respect to the semisymmetric nonmetric connection, then \(M\) is totally geodesic with respect to Levi-Civita connection.
scientific article; zbMATH DE number 6093879