-
defined on the
manifold can be
expressed using the
frame field and its dual
coframe field.
Frame fields were
introduced into
general relativity by
Albert Einstein...
- In mathematics, a
coframe or
coframe field on a
smooth manifold M {\displaystyle M} is a
system of one-forms or
covectors which form a
basis of the cotangent...
-
coordinate expression of the dual
coframe, as
explained in the next section. A
moving frame determines a dual
frame or
coframe of the
cotangent bundle over...
- flat. This
problem reduces to a
question on the
coframe bundle of M.
Suppose we had such a
closed coframe Θ = ( θ 1 , … , θ n ) . {\displaystyle \Theta...
- Cartan, the
primary geometrical information was
expressed in a
coframe or
collection of
coframes on a
differentiable manifold. See
method of
moving frames...
- basis), the
moving coframe (a
moving tangent frame for the
cotangent bundle T ∗ M {\displaystyle \mathrm {T} ^{*}M} ; see also
coframe) {ei}. Then the pseudo-Riemannian...
- PMID 15716951. S2CID 1454595. Nandi, Owi Ivar. 2012.
Human Language Evolution, as
Coframed by
Behavioral and
Psychological Universalisms, Bloomington:
iUniverse Publishers...
- e_{\theta }={\frac {1}{r}}{\frac {\partial }{\partial \theta }},} with dual
coframe e r = d r , e θ = r d θ . {\displaystyle e^{r}=dr,\quad e^{\theta }=rd\theta...
- {\displaystyle c=1} and α = 1 {\displaystyle \alpha =1} , it is
natural to take the
coframe field d σ 0 = x d t , d σ 1 = d x , d σ 2 = d y , d σ 3 = d z {\displaystyle...
-
Kronecker delta. Then Ei is a Maurer–Cartan frame, and θi is a Maurer–Cartan
coframe.
Since Ei is left-invariant,
applying the Maurer–Cartan form to it simply...
