Definition:Normal Projection

Definition

Let $\tilde M$ be a Riemannian manifold.

Let $M \subseteq \tilde M$ be an immersed or embedded Riemannian submanifold.

Let $NM$ be the normal bundle of $M$.

Let $\valueat {T \tilde M} M$ be the tangent bundle of $\tilde M$, but restricted to $M$.

Let $\pi^\perp$ be a smooth bundle homomorphism such that:

$\pi^\perp : \valueat {T \tilde M} M \to NM$

Then $\pi^\perp$ is known as the normal projection.

Sources

• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 2$: Riemannian Metrics. Methods for Constructing Riemannian Metrics