 Normal bundle

For a smooth closed embedding $i:X\hookrightarrow Y$, the normal bundle fits into $0\to TX\to i^{\ast }TY\to N_{X/Y}\to 0$.

In differential geometry, the **normal bundle** is a specific construction associated with an embedded submanifold of a differentiable manifold. It provides a way to understand how the submanifold sits inside the ambient manifold by considering directions that are orthogonal (normal) to the submanifold. ### Definition Let \( M \) be a smooth manifold, and let \( N \subset M \) be a smooth embedded submanifold.