Let （M; H1, H2; Fo） be a SD-splitting for bordered 3-manifold M. The splitting is reducible （weakly reducible, respectively） if there exist essential disks D1 belong to H1 and D2 belong to H2 such that δD1,δD2 belong to Fo and δD1 =δD2 （δD1 ∩ δD2 =φ, respectively）. A SD-splitting （M; H1, H2; Fo） for bordered 3-manifold M is of inner genus 1 if Fo is a punctured torus. In the present paper, we show that a weakly reducible SD-splitting of inner genus 1 is either reducible or bilongitudional.
In this paper, we shall prove that any Heegaard splitting of a δ-reducible 3-manifold M, say M = W U V, can be obtained by doing connected sums, boundary connected sums and self-boundary connected sums from Heegaard splittings of n manifolds M1,..., Mn, where Mi is either a solid torus or an irreducible, δ-irreducible manifold.
