Spectral submanifold

Okay kiddo, imagine you are looking at a rainbow in the sky. You see many different colors like red, orange, yellow, green, blue, and purple. Each of these colors is a part of the rainbow, and together they make up the whole thing that you see.

Well, just like how the rainbow has different parts, a spectral submanifold is a part of a bigger thing called a manifold. A manifold is like a shape that could be flat, like a piece of paper, or it could be curved, like a globe. Spectral submanifolds are found by studying something called the spectrum, which is a set of numbers that are related to the shape of the manifold. These numbers help us understand different properties of the shape, like how it curves or bends.

So, imagine you have a big, curvy shape like a sphere. If you study the spectrum of the sphere, you might find that there are certain ranges of numbers that correspond to different parts of the sphere. These different ranges of numbers make up the spectral submanifolds of the sphere.

Overall, spectral submanifolds are just parts of a bigger shape that can be understood by studying the spectrum of the shape. It's like looking at the different colors of a rainbow to understand how it's made up!