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Results tagged with curvature
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user 118688
Gaussian curvature, mean curvature, sectional curvature, scalar curvature, curvature tensors (Riemann, Ricci, Weyl)
2
votes
0
answers
118
views
Realization of a $\mathfrak{g}$-valued $2$-form as a curvature form
Then, we know that we can construct a principal $S^1$-bundle $P\rightarrow M$ over the manifold $M$, a connection $1$-form $\omega$ on the manifold $P$ such that, the associated curvature form (which is … Under what conditions, can we find a principal $G$ bundle over the manifold $M$, and a connection on $P(M,G)$ whose curvature is $\Omega$? …
- 6,023
1
vote
Accepted
determinant of curvature (notation issue)
Curvature $\Omega$ is a $\mathfrak{g}$ valued $2$-form on $P$ i.e., for each $p\in P$, we have $\Omega(p):T_pP\times T_pP\rightarrow \mathfrak{g}$. …
1
vote
1
answer
213
views
determinant of curvature (notation issue)
Let $\Gamma$ be a connection on $P(M,G)$ and $\Omega$ be its curvature form. This $f_k$ gives a $\mathbb{C}$ valued $2k$ form $f_k(\Omega)$ on $P$. …
- 6,023
3
votes
2
answers
372
views
holonomy of connection on gerbes
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We call the closed $3$ form $G$ the curvature of the gerbe connection.
We say that a connection on a gerbe is flat if its curvature $G$ vanishes. …
- 6,023