# On $(1,1)$-tensor fields on symplectic manifolds

Archivum Mathematicum (1999)

- Volume: 035, Issue: 4, page 329-336
- ISSN: 0044-8753

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topDekrét, Anton. "On $(1,1)$-tensor fields on symplectic manifolds." Archivum Mathematicum 035.4 (1999): 329-336. <http://eudml.org/doc/248373>.

@article{Dekrét1999,

abstract = {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.},

author = {Dekrét, Anton},

journal = {Archivum Mathematicum},

keywords = {symplectic structure; natural lifts on tangent and cotangent bundles; symplectic structure; natural lifts on tangent and cotangent bundles},

language = {eng},

number = {4},

pages = {329-336},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {On $(1,1)$-tensor fields on symplectic manifolds},

url = {http://eudml.org/doc/248373},

volume = {035},

year = {1999},

}

TY - JOUR

AU - Dekrét, Anton

TI - On $(1,1)$-tensor fields on symplectic manifolds

JO - Archivum Mathematicum

PY - 1999

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 035

IS - 4

SP - 329

EP - 336

AB - 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.

LA - eng

KW - symplectic structure; natural lifts on tangent and cotangent bundles; symplectic structure; natural lifts on tangent and cotangent bundles

UR - http://eudml.org/doc/248373

ER -

## References

top- Liftings of tensor fields to the cotangent bundle, Proceedings, Int. conference Diff. Geometry and Applications Brno (1996), MU Brno, 141–150. (1996) MR1406334
- 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. (1996) MR1463514
- Lifts of some tensor fields and connections to product preserving functors, 135 (1914), Nagoya Math. J., 1–41. (1914) MR1295815
- Symplectic Geometry and Analytical Mechanics, (1987), D. Reider Pub. Comp., Dortrecht - Boston - Lancaster - Tokyo. (1987) MR0882548
- Tangent and cotangent bundles, M. Dekker Inc. New York, 1973. (1973) MR0350650

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