Normal bundle
Okay kiddo, imagine you're standing on a straight line, like a tightrope walker. The line is the "manifold" and it's what we use to describe the shape of a space. Now, you can move your arms and legs around, but you have to stay on the line.
The normal bundle is like a little cushion that sits on the line right where you're standing. It has a direction, like an arrow, that points straight out from the line. This direction shows which way you could step off the line without falling down.
The normal bundle is important because it helps us understand how things move and interact on the line. If we're studying something that's moving along the line, we can use the normal bundle to see how it's related to the line itself. It's like we're looking at two things at once - the thing that's moving and the line it's moving on.
So, in summary, the normal bundle is a way to understand how things on a line are related to the line itself, and how they move in relation to it.
The normal bundle is like a little cushion that sits on the line right where you're standing. It has a direction, like an arrow, that points straight out from the line. This direction shows which way you could step off the line without falling down.
The normal bundle is important because it helps us understand how things move and interact on the line. If we're studying something that's moving along the line, we can use the normal bundle to see how it's related to the line itself. It's like we're looking at two things at once - the thing that's moving and the line it's moving on.
So, in summary, the normal bundle is a way to understand how things on a line are related to the line itself, and how they move in relation to it.