For a homework assignment i was asked to proof that the positive cone {x^2 + y^2 = z^2, z>= 0} cannot be a submanifold of any dimension of R^3.(adsbygoogle = window.adsbygoogle || []).push({});

It apparently goes wrong at the origin. I guess it's because you can't really speak of a tangent space at that point. So I tried to prove by contradiction you can't have a tangent space at that point. But I couldn't really arrive at a contradiction

Could someone give me a hint?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Cone as submanifold of R^3

**Physics Forums | Science Articles, Homework Help, Discussion**