you said " But over any point where there are n linearly independent sections they span the fiber. Over another point where they are independent they also space the fiber " . you want to say dependent, they also generate the vector bundle ?
If I understand what you mean, a family of sections can be generating a vector bundle at a point that if they are linearly independent
"" It cannot span the fiber above a point where they are not linearly independent. ""
My problem is: if a family of sections generate E_ {x1}? is that this family engandrent E_ {x2} or any other fiber, or a family of sections if (free generator, form a basis ...) is that above all point x variety, (S_{1}, ...,s_{n}) are kept the same properties?
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...
Hello friends, I am looking for an idea to my exercise!
let's E be a vector space, e_ {i} be a basis of E, b_ {a} an element of E then
b_ {a} = b_ {a} ^ {i} e_ {i}.
I want to define a family of vectors {t_ {i}}, that lives on E , (how to choose this family already, it must not be a...
let x a point on complex manifold X, z_j a coordinate system at x , E a holomorphic bundle and let h_α be a holomorphic frame of E. After replacing h_α by suitable linear combinations with constant coefficients we may assume that h_ α is an orthonormal basis of E_{x}. Then an inner product <h_α...
hi friends,
Suppose we have a vector bundle E equipped with a hermitian metric h, and in a subbundle of E noted SE . I would like tocalculate explicitly the induced metric Sh defined on SE. How to proceed?
"I have another question now, if we have a vector bundle E1 with a metric g1 and E2 a vector bundle with a metric g2, what will be the metric on the product?
I have another question now, if we have a vector bundle with a metric E1 G1 and E2 a vector bundle with a metric g2, it will be the metric on the product?
yes I speak of a normed vector space, but how you got this metric? you can give me the link or document where I can find the information?
and thank you very much.
Hello friends,
I would ask if anyone knows the métrqiue on the quotient space? ie, if one has a metric on a vector space, how can we calculate the metric on the quotient space of E?
Hi friends !
Let E be a holomorphic vector bundle over a complex manifold M . We identify M with the zero section of E .
i would like to know waht's mean "" We identify M with the zero section of E ".
thnx :)
hi friends !
it is well known that a Lie algebra over K is a K-vector space g equipped
of a K-bilinear, called Lie bracket. I ask how can we determines the Lie algebra of any vector space then? For example we try the Lie algebra of horizontal space.