Splitting Theorems for Submanifolds of Nonnegative Isotropic Curvature

We study isometric immersions of complete manifolds of nonnegative isotropic curvature that have spaces of relative nullity. These manifolds decompose into a Riemannian product ${\bar{M}\times \mathbb R^k}$ . In the case that k??? 2, we use recent results of Brendle-Schoen to completely classify these manifolds. We then apply this classification to study complete non-compact K?hler submanifolds with relatively low codimension.