Differentiable Manifold

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  • #1
atomqwerty
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Homework Statement


In which points the surface [tex]\{\left(x,y,z\right)\in\Re^{3}|x^{3}-y^{3}+xyz-xy=0\right\}[/tex] is a differentiable manifold (subvariedad diferenciable in spanish). Calculate its tangent space in the point (1,1,1).


Homework Equations



NA

The Attempt at a Solution



I've been several problems with the definition of Subvariedad - I don't know if it's said Manifols in english

Thank you
 

Answers and Replies

  • #2
hunt_mat
Homework Helper
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Write the surface in the form z=f(x,y) and look for points where z becomes undefined.
Do they want the tangent space or tangent plane? For the latter, it is just the plane perpendicular to [tex]\nabla (x^{3}-y^{3}+xyz-xy)[/tex], fot the former it's slightly more complicated
 
  • #3
atomqwerty
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It was the space. Thank you so much :)
 

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