Please help, construct a natural differential structure on this manifoldby saminator910 Tags: construct, differential, manifold, natural, structure 

#1
Dec3112, 11:01 AM

P: 79

I need to construct a natural smooth differential structure on the ellipsoid [(x^2)/(a^2)]+[(y^2)/(b^2)]+[(z^2)/(c^2)]=1
So I need an Atlas to produce this, how would I do this? I don't really have an idea of what functions and sets an Atlas consists of, can one use parametric equations? Also, is this diffeomorphic to S^2? There needs to be a smooth mapping from the ellipsoid to the 2sphere, correct? 


Register to reply 
Related Discussions  
Diffeomorphisms, Differential Structure, ETC.  Differential Geometry  17  
Differential manifold without connection: Is it possible?  Differential Geometry  9  
Differential Equation Involving Natural Log.  Calculus & Beyond Homework  1  
Hausdorff condition in differential manifold definition  Differential Geometry  2  
Differential Topology: 1dimensional manifold  Calculus & Beyond Homework  7 