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symplectic structure; natural lifts on tangent and cotangent bundles
Two symplectic structures on a manifold $M$ determine a (1,1)-tensor field on $M$. In this paper we study some properties of this field. Conversely, if $A$ is (1,1)-tensor field on a symplectic manifold $(M, \omega )$ then using the natural lift theory we find conditions under which $\omega ^A, \omega ^A(X, Y)=\omega (AX, Y)$, is symplectic.
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