# Article

 Title: On $(1,1)$-tensor fields on symplectic manifolds (English) Author: Dekrét, Anton Language: English Journal: Archivum Mathematicum ISSN: 0044-8753 (print) ISSN: 1212-5059 (online) Volume: 35 Issue: 4 Year: 1999 Pages: 329-336 Summary lang: English . Category: math . Summary: 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. (English) Keyword: symplectic structure Keyword: natural lifts on tangent and cotangent bundles MSC: 37J05 MSC: 53D05 MSC: 58A20 idZBL: Zbl 1054.53089 idMR: MR1744520 . Date available: 2008-06-06T22:24:46Z Last updated: 2012-05-10 Stable URL: http://hdl.handle.net/10338.dmlcz/107707 . Reference: [1] Doupovec, M., Kurek, J.: Liftings of tensor fields to the cotangent bundle.Proceedings, Int. conference Diff. Geometry and Applications Brno (1996), MU Brno, 141–150. MR 1406334 Reference: [2] Doupovec, M., Kurek, J.: Liftings of covariant (0,2)-tensor fields to the bundle of $k$-dimensional 1-velocities.Supplements di Rendiconti del Circolo Matematico di Palermo, Serie II 43 (1996), 111–121. MR 1463514 Reference: [3] Gancarzewicz, J., Mikulski, W., Pogoda, Z.: Lifts of some tensor fields and connections to product preserving functors.135 (1914), Nagoya Math. J., 1–41. MR 1295815 Reference: [4] Libermann, P., Marle, Ch.: Symplectic Geometry and Analytical Mechanics.(1987), D. Reider Pub. Comp., Dortrecht - Boston - Lancaster - Tokyo. MR 0882548 Reference: [5] Yano, K., Ishihara, S.: Tangent and cotangent bundles.M. Dekker Inc. New York, 1973. MR 0350650 .

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