Geodesic
On $(1,1)$-tensor fields on symplectic manifolds
Archivum mathematicum, Tome 35 (1999) no. 4, pp. 329-336

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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.
Classification : 37J05, 53D05, 58A20
Keywords: symplectic structure; natural lifts on tangent and cotangent bundles 
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     author = {Dekr\'et, Anton},
     title = {On $(1,1)$-tensor fields on symplectic manifolds},
     journal = {Archivum mathematicum},
     pages = {329--336},
     publisher = {mathdoc},
     volume = {35},
     number = {4},
     year = {1999},
     mrnumber = {1744520},
     zbl = {1054.53089},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1999__35_4_a4/}
}
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Dekrét, Anton. On $(1,1)$-tensor fields on symplectic manifolds. Archivum mathematicum, Tome 35 (1999) no. 4, pp. 329-336. http://geodesic.mathdoc.fr/item/ARM_1999__35_4_a4/