Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 118 / 4 / a

Table of contents
- Solution a

Solution

A connection on a vector bundle is a complex-linear map

D : Ω^{0} (E) \to Ω^{1} (E)

satisfying the Leibniz rule

D (f s) = df \otimes s + f Ds

. It is compatible with the Hermitian metric on a holomorphic vector bundle

h

when

d h (s, t) = h (Ds, t) + h (s, D t),

and compatible with the holomorphic structure when its type-

(0, 1)

part is the Dolbeault partial connection:

D^{0, 1} = \overset{ˉ}{\partial}_{E} .

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version