Is there a smooth covector field on
that is exact and vanishes at exactly one point?
I think the answer is no...
in case of exact field we have
for some smooth function on
... it vanishes at some point
when partial derivatives of
at p are equal to zero (in some chart containing
).
..is it correct to say that if we consider stereographic coordinates on
then for any point
where
vanishes it will also vanish at point
??