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6 votes
1 answer
734 views

Are the Sasaki metrics on tangent and cotangent bundle isomorphic?

Let $(M,g)$ be a Riemannian manifold. Then there is the well-known Sasaki metric that makes $(TM,\hat{g})$ a Riemannian manifold. In a similar way, one can construct a Sasaki metric $\bar{g}$ on the ...
Jaap Eldering's user avatar
1 vote
2 answers
2k views

tangent and cotangent bundle

Hi, I am reading "Introduction to symplectic topology" by McDuff and salamon. At some point I cant go further. My question is: Let $(M,g)$ be a Riemannian manifold and consider the cotangent bundle $T^...
marco's user avatar
  • 11
1 vote
1 answer
97 views

Derivative of the symplectomorphism evaluated at a point of the zero section of the cotangent bundle

It might be an easy question, possibly not worth posting here. In the proof of the Lagrangian neighborhood theorem, the authors have written the expression for the derivative of a symplectomorphism at ...
Random's user avatar
  • 1,097