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

Anton Dekrét

Archivum Mathematicum (1999)

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

Abstract

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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 , ω ) then using the natural lift theory we find conditions under which ω A , ω A ( X , Y ) = ω ( A X , Y ) , is symplectic.

How to cite

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Dekrét, 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

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  1. Liftings of tensor fields to the cotangent bundle, Proceedings, Int. conference Diff. Geometry and Applications Brno (1996), MU Brno, 141–150. (1996) MR1406334
  2. 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
  3. Lifts of some tensor fields and connections to product preserving functors, 135 (1914), Nagoya Math. J., 1–41. (1914) MR1295815
  4. Symplectic Geometry and Analytical Mechanics, (1987), D. Reider Pub. Comp., Dortrecht - Boston - Lancaster - Tokyo. (1987) MR0882548
  5. Tangent and cotangent bundles, M. Dekker Inc. New York, 1973. (1973) MR0350650

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