Canonical Lift on Cotangent Bundles
There exists an operation, that we call canonical lift and denote by a “hat” ^, which creates “symplectic objects” on a cotangent bundle T*Q starting from “objects” on the manifold Q (vector fields,maps,submanifolds, etc.). It plays an important role in the theory of symplectic relations and in its applications. The basic lift, from which all other canonical lifts can be derived, is that of a submanifold.
KeywordsCotangent Bundle Lagrangian Submanifold Vertical Vector Symplectic Reduction Canonical Lift
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