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ON (1,1)-TENSOR FIELDS ON SYMPLECTIC MANIFOLDS

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*Anton Dekrét*

**Address.** Department of Mathematics, TU Zvolen Masarykova 24, 960
53 Zvolen, SLOVAKIA
**E-mail:** dekret@vsld.tuzvo.sk

**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.

**AMSclassification.** 53C05, 58A20

**Keywords.** Symplectic structure, natural lifts on tangent and
cotangent bundles