# 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=M*_{D}× M_{D⊥ }, where *M*_{D} is an invariant submanifold of *M* and *M*_{D⊥ } is an antiinvariant submanifold of *M*. Some other properties regarding the immersion *x:M→ N* are discussed.