1. ## Examples of Manifold

Which of the following are manifolds :

1) a sphere
2) a cone
3) an ellipse
4) a pair of intersecting planes

and which of the above are differential manifolds and why?

2. ## Re: Examples of Manifold

Do you understand what a manifold is? What a differentiable manifold is? What are your thoughts about this problem, and where are you unsure/confused?

3. ## Re: Examples of Manifold

Those are all manifolds, but not all differentiable manifolds. It is possible that your text is dealing only with differentiable manifolds and so just calls them "manifolds".

What definition of "manifold" are you using?

4. ## Re: Examples of Manifold

I don't think (d) means the intersection of a pair of intersecting planes (which would be either a line or a plane, hence a manifold), but rather means the union of two planes that happen to intersect (which will not be a manifold - unless the planes are the same).

5. ## Re: Examples of Manifold

Originally Posted by johnsomeone
I don't think (d) means the intersection of a pair of intersecting planes (which would be either a line or a plane, hence a manifold), but rather means the union of two planes that happen to intersect (which will not be a manifold - unless the planes are the same).
That's the way I would interpret it.