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