A submanifold in $P^n$ with parallel normal subbundle which is normalized in the sense of Norden

The concept of a $p$-dimensional parallel subbundle of the normal bundle of a submanifold $V^m$ of $n$-dimensional protective space $P^n$ normalized in the sense of Norden [1] is introduced. The local structure of such manifolds is studied. The structure is also investigated of submanifolds $V^m$ which have normal subbundles with a flat projective connection. Their structure is closely related with the structure of tangentially degenerate submanifolds [2, 3] and submanifolds admitting a dual normalization [4].