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

100%

Dacko P., Olszak Z.

Open Mathematics

2005

tom 3

nr 2

318-330

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 $$\mathcal{D}$$ -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, and it is noted that a given almost cosymplectic (−1, μ 0)-space is locally isomorphic to a corresponding model. In the case when μ is constant, the models can be constructed on the whole of ℝ2n+1 and it is shown that they are left invariant with respect to Lie group actions.

On almost cosymplectic (κ,μ,ν)-spaces

100%

Dacko P., Olszak Z.

Banach Center Publications

2005

tom 69

nr 1

211-220

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 𝓓-homothetic transformations of almost cosymplectic structures. For such manifolds, the tensor fields φ, h ($= (1/2)ℒ_{ξ}φ$), A ( = -∇ξ) fulfill a certain system of differential equations. It is proved that the leaves of the canonical foliation of an almost cosymplectic (κ,μ,ν)-space with κ<0 are locally flat Kählerian manifolds. A local characterization of such manifolds is established up to a 𝓓-homothetic transformation of the almost cosymplectic structures.

Ograniczanie wyników

1 Banach Center Publications

1 Open Mathematics

2 Dacko P.

2 Olszak Z.

2 2005

Wyniki wyszukiwania

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

On almost cosymplectic (κ,μ,ν)-spaces