# Examples of Manifold

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• Sep 24th 2012, 12:04 PM
manik
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?
• Sep 24th 2012, 01:59 PM
johnsomeone
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?
• Sep 26th 2012, 07:55 AM
HallsofIvy
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?
• Sep 26th 2012, 10:05 AM
johnsomeone
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).
• Sep 29th 2012, 11:54 AM
HallsofIvy
Re: Examples of Manifold
Quote:

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.