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?

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- September 24th 2012, 01:04 PMmanikExamples 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? - September 24th 2012, 02:59 PMjohnsomeoneRe: 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?

- September 26th 2012, 08:55 AMHallsofIvyRe: 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? - September 26th 2012, 11:05 AMjohnsomeoneRe: 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).

- September 29th 2012, 12:54 PMHallsofIvyRe: Examples of Manifold