- Cartan, the
primary geometrical information was
expressed in a
coframe or
collection of
coframes on a
differentiable manifold. See
method of
moving frames...
- 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...
- zero). In fact, in the
method of
moving frames, one more
often works with
coframes rather than frames. More generally,
moving frames may be
viewed as sections...
- ^{n}).} If we had
another coframe Φ = ( ϕ 1 , … , ϕ n ) {\displaystyle \Phi =(\phi ^{1},\dots ,\phi ^{n})} , then the two
coframes would be
related by an...
-
Cambridge University Press. ISBN 0-521-42908-0. See
Chapter 4 for
frames and
coframes. If you ever need more
information about frame fields, this
might be a...
- 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...
- \tau }(0){\bigr ]}x^{\tau }+O(|x|^{2}).}
Similarly we can
construct local coframes in
which e μ ∗ a ( x ) = δ a μ − 1 6 R a σ μ τ ( 0 ) x σ x τ + O ( x 2...
- two-manifold is to use the
differential forms method of Élie Cartan. Take the
coframe field σ 1 = exp ( p ) d x , σ 2 = exp ( p ) d y {\displaystyle \sigma...
