Recent content by math6

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...

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?

Thank you for your answers.

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.

Livinia thank you, I finally found the answer. :)

a sphere is orientable if and only if it admits a volume form. If you're in a Riemannian manifold then the volume form is well known. Or you can use the definition of orientability of a manifold, a manifold is orientable if \ det (\ frac {\ partial x ^ {i}} {{partial y ^ {i}})> 0 for two...