In this joint work with Xianghong Gong (Wisconsin-Madison U.), we show that an $n$-dimensional complex torus embedded in a complex manifold of dimensional $n+d$, with a split tangent bundle, has a neighborhood biholomorphic to a neighborhood of the zero section in its normal bundle, provided the latter has (locally constant) Hermitian transition functions and satisfies a {\it non-resonant Diophantine} condition. This generalizes works by Arnold and Il'yashenko-Pyartli.