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Connections induced by ( 1 , 1 ) -tensor fields on cotangent bundles

Anton Dekrét — 1998

Mathematica Bohemica

On cotangent bundles the Liouville field, the Liouville 1-form ε and the canonical symplectic structure d ε 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.

On skew 2-projectable almost complex structures on T M

Anton Dekrét — 1998

Archivum Mathematicum

We deal with a ( 1 , 1 ) -tensor field α on the tangent bundle T M preserving vertical vectors and such that J α = - α J is a ( 1 , 1 ) -tensor field on M , where J is the canonical almost tangent structure on T M . A connection Γ α on T M is constructed by α . It is shown that if α is a V B -almost complex structure on T M without torsion then Γ α is a unique linear symmetric connection such that α ( Γ α ) = Γ α and Γ α ( J α ) = 0 .

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