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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 .

On ( 1 , 1 ) -tensor fields on symplectic manifolds

Anton Dekrét — 1999

Archivum Mathematicum

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 , ω ) then using the natural lift theory we find conditions under which ω A , ω A ( X , Y ) = ω ( A X , Y ) , is symplectic.

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