- #1
math6
- 67
- 0
Hi Friends
my little problem is :
Let E be a vector bundle over a manifold M, and (s_ {1}, ..., s_ {n}) a family of sections of E. This family is generating bundle E, that is for every point x in M, (s_ {1} (x), ..., s_ {n} (x)) is generator of the vector space E_{x} ? is that we have only (s_ {1} (x1), ..., s_ {n} (x1)) is a generator of E_ {x1} and (s_ {1} (x 2), .. ..., s_ {n} (x2)) is not generating E_ {x2}??
Thank you for making me understand this confusion on sections of a vector bundle generator ...
my little problem is :
Let E be a vector bundle over a manifold M, and (s_ {1}, ..., s_ {n}) a family of sections of E. This family is generating bundle E, that is for every point x in M, (s_ {1} (x), ..., s_ {n} (x)) is generator of the vector space E_{x} ? is that we have only (s_ {1} (x1), ..., s_ {n} (x1)) is a generator of E_ {x1} and (s_ {1} (x 2), .. ..., s_ {n} (x2)) is not generating E_ {x2}??
Thank you for making me understand this confusion on sections of a vector bundle generator ...