Differential Geometry

Question

Question

Let S²={(x,y,z) ∈R³| x²+y²+z²=1}, and B={(x,y) ∈R²| x²+y²<1} show that the map

f:B → S², f(x,y)=(x,y,√(1-x^2-y²)) is a smooth diffeomorphism on an open set W

W={(x,y,z) ∈S²⊂R³| z>0} ⊂S².

Diffeomorphism

Answer 1

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