Let \(M_1, \ldots , M_k\) denote smooth manifolds of dimension \(n_1,\ldots ,n_k\), respectively. The product manifold \(M_1\times \cdots \times M_k\) with the product smooth manifold structure is a smooth manifold.
Examples
- \(n\)-torus
Let \(M_1, \ldots , M_k\) denote smooth manifolds of dimension \(n_1,\ldots ,n_k\), respectively. The product manifold \(M_1\times \cdots \times M_k\) with the product smooth manifold structure is a smooth manifold.