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

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