Submanifolds of an even-dimensional manifold structured by a T-parallel connection
(Lobachevskii Journal of Mathematics, Volume XIII)
Even-dimensional manifolds N structured by a T-parallel connection have been defined and studied in [DR], [MRV]. In the present paper, we assume that N carries a (1,1)-tensor field J of square -1 and we consider an immersion x:M→ N. It is proved that any such M is a CR-product [B] and one may decompose M as M=MD× MD⊥ , where MD is an invariant submanifold of M and MD⊥ is an antiinvariant submanifold of M. Some other properties regarding the immersion x:M→ N are discussed.