On canonical forms on non-holonomic and semi-holonomic prolongations of principal fibre bundles
On cotangent bundles the Liouville field, the Liouville 1-form and the canonical symplectic structure d exist. In this paper interactions between these objects and -tensor fields on cotangent bundles are studied. Properties of the connections induced by the above structures are investigated.
We deal with a -tensor field on the tangent bundle preserving vertical vectors and such that is a -tensor field on , where is the canonical almost tangent structure on . A connection on is constructed by . It is shown that if is a -almost complex structure on without torsion then is a unique linear symmetric connection such that and .
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