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Q.2 in the text. By the hint I have shown that it has 2 tangent directions. Now how does it follows that there is no submersion?enter image description here

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Because $df_p$ sends two linearly independent vectors (which therefore span $\Bbb R^2$) to $0$.

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  • $\begingroup$ Thanks for the answer. $\endgroup$ – Abhi7731756 Mar 23 at 16:44
  • $\begingroup$ You're welcome. Welcome to MSE. If you’re satisfied with the answer, you should accept it so the question doesn't stay on the unanswered list. $\endgroup$ – Ted Shifrin Mar 23 at 17:49

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