Connections induced by (1,1)-tensor fields on cotangent bundles. (English) Zbl 0934.53020

Dekrét, Anton

Math. Bohem. 123, No. 3, 317-331 (1998).

Summary: On cotangent bundles the Liouville field, the Liouville 1-form \(\varepsilon \) and the canonical symplectic structure d\(\varepsilon \) exist. In this paper, interactions between these objects and \((1,1)\)-tensor fields on cotangent bundles are studied. Properties of the connections induced by the above structures are investigated.

MSC:

53C05	Connections (general theory)
53D05	Symplectic manifolds (general theory)

Keywords:

connection; almost complex structure; tensor field; Liouville field; canonical symplectic structure