All Questions
8 questions
8
votes
0
answers
480
views
Connections and curvature in commutative algebra
Since on any commutative algebra $R$ over ring $S$ we have module of Kahler differentials $(\Omega_{R/S},d)$ which extends to the algebraic de-Rham complex $(\Omega^\bullet,d),$ it is natural to ...
- 1,615
7
votes
1
answer
1k
views
Differential forms along the fiber
Let $E \to M$ be a smooth fiber bundle. Instead of differential forms defined on the whole tangent bundle $TE$ one could also consider forms on the vertical tangent bundle $VE$, i.e. forms defined on ...
- 5,824
7
votes
1
answer
296
views
ASD connection for Line bundle over $4$-manifold
Let $(M,g)$ be an oriented closed Riemannian $4$ manifold.
Let $L\to M$ be a complex line bundle.
Q Under what condition, we can find an ASD connection of $L$, i.e. a connection $A$ such that $F^+...
- 1,915
3
votes
4
answers
3k
views
References on principal G bundle and connections
I am trying to understand about principal G bundle given a Lie group $G$. For that, I started with the action of Lie groups on manifold $M$ and convinced myself that if the action is smooth, proper, ...
- 6,023
3
votes
0
answers
238
views
Parallel Ricci condition - Status report and bibliography
First I'd like to point out that I'm not a mathematician but a physicist. Dealing with a (hopefully) new affine theory of gravity we have find that the equation of motion are not the usual Einstein's ...
- 690
2
votes
0
answers
71
views
Covariant momenta associated to higher order Lagrangians
Let $\pi:Y\rightarrow X$ be a fibered manifold with fibered coordinates $(U,x^i,y^\rho)$ (whenever local calculations are needed) and $m$ dimensional base $X$ ($\dim X=m$).
Suppose that $L\in\Omega^m_{...
- 2,792
1
vote
1
answer
231
views
The bundle of symmetric affine connections as quotient of the second-order frame bundle
This post is not about finding an answer to a certain problem - because the answer already exists - but rather about finding the simplest possible answer.
The problem is: how to define the bundle $C(...
- 2,527
0
votes
2
answers
435
views
Isomorphism of connections on a complex line bundle
Reading an article I faced with the following theorem, please give me a reference to a proof of the fact which is stated without any reference in the article. Is it a well-known fact?
Theorem. Let $E ...
- 1,329