On contact embeddings of contact manifolds in the odd dimensional Euclidean spaces

Abstract

We prove that a closed co-oriented contact (2m + 1)-manifold (M2m + 1, ξ) can be a contact submanifold of the standard contact structure on ℝ4m + 1, if it satisfies one of the following conditions: (1) m is odd (m ≥ 3) and H1(M2m + 1; ℤ) = 0, (2) m is even (m ≥ 4) and M2m + 1 is 2-connected, (3) m = 2 and M5 is simply-connected.