1. Like the tangent bundle the cotangent bundle is again a differentiable manifold. 2. The cylinder is the cotangent bundle of the circle. 3. The cotangent bundle has a canonical canonical one-form, the symplectic potential. 4. In that case, ? 1 is called the cotangent bundle of " X ". 5. Likewise, a 1-form on " M " is a section of the cotangent bundle . 6. :I didn't think that one out, T * S3 is the Cotangent bundle , see here. 7. On a ( pseudo-) Riemannian manifold, the geodesic flow is identified with a Hamiltonian flow on the cotangent bundle . 8. For the cotangent bundle of a manifold M, the Floer homology depends on the choice of Hamiltonian due to its noncompactness. 9. Thus we can regard covector fields not just as sections of the cotangent bundle , but also linear mappings of vector fields into functions. 10. The existence of such a vector field on " TM " is analogous to the canonical one-form on the cotangent bundle .
