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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:
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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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