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Vector fields and connection on fibred manifolds

Dekrét, Anton — 1990

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0699.00032.] In a previous paper [Cas. Pestovani Mat. 115, No.4, 360-367 (1990)] the author determined the set of the vector fields on TM by which connections on TM can be constructed. In this paper, he generalizes some of such constructions to the case of vector fields on fibred manifolds, giving several examples.

On canonical forms on non-holonomic and semi-holonomic prolongations of principal fibre bundles

Anton Dekrét — 1972

Czechoslovak Mathematical Journal

On quasi-Riemannian fiber manifold

Anton Dekrét — 1981

Czechoslovak Mathematical Journal

On bilinear structures on differentiable manifolds

Anton Dekrét — 1979

Archivum Mathematicum

On connections on the second iterated tangent bundle

Anton Dekrét — 1987

Archivum Mathematicum

On forms and connections on fibre bundles

Anton Dekrét — 1980

Časopis pro pěstování matematiky

On quasi-jets

Anton Dekrét — 1986

Časopis pro pěstování matematiky

Vector fields and connections on $T M$

Anton Dekrét — 1990

Časopis pro pěstování matematiky

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 $\nabla_{Γ_{α}} (J α) = 0$ .

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.