Regular submanifold
Okay kiddo, imagine you have a big ball that's covered with a lot of dirt. Now you want to clean it up but you don't want to touch the ball directly because you might damage it. So, you decide to use a cloth to clean it up. But the cloth is not a perfect fit for the ball so it doesn't cover all the ball's surface. Instead, it only touches some parts of the ball, leaving others untouched.
Now let's imagine that the ball is like a mathematical object called a manifold. A manifold is just a fancy word for a shape that can be stretched and bent like a rubber sheet. And the cloth is like a smaller shape that we call a submanifold.
A regular submanifold is a submanifold where the cloth fits perfectly on the ball's surface. Imagine that we carefully cut a smaller ball-shaped patch from the cloth and then stretch and mold it to perfectly fit onto the ball's surface.
Similarly, a regular submanifold is a smaller shape that fits perfectly onto a larger shape without any wrinkling or overlapping. It's like a mathematical puzzle piece that fits perfectly into its place. In this way, we can use regular submanifolds to describe the different shapes and surfaces in math and science.
Now let's imagine that the ball is like a mathematical object called a manifold. A manifold is just a fancy word for a shape that can be stretched and bent like a rubber sheet. And the cloth is like a smaller shape that we call a submanifold.
A regular submanifold is a submanifold where the cloth fits perfectly on the ball's surface. Imagine that we carefully cut a smaller ball-shaped patch from the cloth and then stretch and mold it to perfectly fit onto the ball's surface.
Similarly, a regular submanifold is a smaller shape that fits perfectly onto a larger shape without any wrinkling or overlapping. It's like a mathematical puzzle piece that fits perfectly into its place. In this way, we can use regular submanifolds to describe the different shapes and surfaces in math and science.