cotangent bundle उदाहरण वाक्य

उदाहरण वाक्य

1. In differential geometry, a "'one-form "'on a differentiable manifold is a section of the cotangent bundle.
2. where V _ \ Sigma Y and V _ \ Sigma ^ * Y are the vertical cotangent bundle of Y \ to \ Sigma.
3. The 1-form is a section of the cotangent bundle, that gives a local linear approximation to in the cotangent space at each point.
4. While the upper bound is an immediate consequence of the above interpretation of in terms of the cotangent bundle, the lower bound is more subtle.
5. If is a real differentiable function over, then is a section of the cotangent bundle and as such, we can construct a map from to.
6. The exterior derivative of & theta; is a Hamiltonian; thus the cotangent bundle can be understood to be a phase space on which Hamiltonian mechanics plays out.
7. Another classical case occurs when M is the cotangent bundle of \ mathbb { R } ^ 3 and G is the Euclidean group generated by rotations and translations.
8. Let N be a smooth manifold and let T ^ * N be its cotangent bundle, with projection map \ pi : T ^ * N \ rightarrow N.
9. There are more complicated operations on the Floer homology of a cotangent bundle that correspond to the string topology operations on the homology of the loop space of the underlying manifold.
10. The cotangent bundle of a differentiable manifold consists, at every point of the manifold, of the dual of the tangent space, the cotangent space . differential one-forms.