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On compact holomorphically pseudosymmetric Kählerian manifolds

Zbigniew Olszak — 2009

Open Mathematics

For compact Kählerian manifolds, the holomorphic pseudosymmetry reduces to the local symmetry if additionally the scalar curvature is constant and the structure function is non-negative. Similarly, the holomorphic Ricci-pseudosymmetry reduces to the Ricci-symmetry under these additional assumptions. We construct examples of non-compact essentially holomorphically pseudosymmetric Kählerian manifolds. These examples show that the compactness assumption cannot be omitted in the above stated theorem....

On almost cosymplectic (−1, μ, 0)-spaces

Piotr DackoZbigniew Olszak — 2005

Open Mathematics

In our previous paper, almost cosymplectic (κ, μ, ν)-spaces were defined as the almost cosymplectic manifolds whose structure tensor fields satisfy a certain special curvature condition. Amongst other results, it was proved there that any almost cosymplectic (κ, μ, ν)-space can be 𝒟 -homothetically deformed to an almost cosymplectic −1, μ′, 0)-space. In the present paper, a complete local description of almost cosymplectic (−1, μ, 0)-speces is established: “models” of such spaces are constructed,...

On almost cosymplectic (κ,μ,ν)-spaces

Piotr DackoZbigniew Olszak — 2005

Banach Center Publications

An almost cosymplectic (κ,μ,ν)-space is by definition an almost cosymplectic manifold whose structure tensor fields φ, ξ, η, g satisfy a certain special curvature condition (see formula (eq1b)). This condition is invariant with respect to the so-called -homothetic transformations of almost cosymplectic structures. For such manifolds, the tensor fields φ, h ( = ( 1 / 2 ) ξ φ ), A ( = -∇ξ) fulfill a certain system of differential equations. It is proved that the leaves of the canonical foliation of an almost cosymplectic...

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