cotangent bundle उदाहरण वाक्य

उदाहरण वाक्य

1. If one considers a Riemannian manifold or a pseudo-Riemannian manifold, the Riemannian metric induces a linear isomorphism between the tangent and cotangent bundles . ( See Musical isomorphism ).
2. where the ? " i " are the fiber coordinates on the cotangent bundle induced by the coordinate differentials d " x " " i ".
3. where ? is the holomorphic cotangent bundle and the notation ? [ 2 ] means the " tensor square " ( " not " the second exterior power ).
4. Sikorav is known for his proof, joint with Fran�ois Laudenbach, of the Arnold conjecture for Lagrangian intersections in cotangent bundles, as well as for introducing generating families in symplectic topology.
5. A volume form is a nowhere vanishing section & omega; of \ bigwedge ^ n T ^ * M, the top exterior power of the cotangent bundle of " M ".
6. The explanation in geometric terms is that a general tensor will have contravariant indices as well as covariant indices, because it has parts that live in the tangent bundle as well as the cotangent bundle.
7. Thus, every " frame field " is associated with a unique " coframe field ", and vice versa; a coframe fields is a set of four orthogonal sections of the cotangent bundle.
8. The associated graded algebra is the commutative algebra of smooth functions on the cotangent bundle T ^ * M which are polynomial along the fibers of the projection \ pi \ colon T ^ * M \ rightarrow M.
9. Just as we build differential forms out of exterior powers of the cotangent bundle, we can build exterior powers of the complexified cotangent bundle ( which is canonically isomorphic to the bundle of dual spaces of the complexified tangent bundle ).
10. Just as we build differential forms out of exterior powers of the cotangent bundle, we can build exterior powers of the complexified cotangent bundle ( which is canonically isomorphic to the bundle of dual spaces of the complexified tangent bundle ).