Please help, construct a natural differential structure on this manifold

by saminator910
Tags: construct, differential, manifold, natural, structure
saminator910 is offline
Dec31-12, 11:01 AM
P: 78
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 2-sphere, correct?
Phys.Org News Partner Science news on
Going nuts? Turkey looks to pistachios to heat new eco-city
Space-tested fluid flow concept advances infectious disease diagnoses
SpaceX launches supplies to space station (Update)

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: 1-dimensional manifold Calculus & Beyond Homework 7