The problem is to show that the cone $ z^2= x^2+y^2$ is not an immersed smooth manifold in $\mathbb{R}^3$.
The cone is not immersed in $\mathbb{R}^3$
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differential-geometry
differential-topology
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1Do you have a question? Your 2nd sentence does not quite make sense. – 2012-05-15
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0This result is false for dimension 2, but the question is about dimension 3. – 2012-05-15
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0Sorry but show that something is an immersion is more reasonable, but show that it is not is a totally different approach. – 2012-05-20