Abstract
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.
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Dacko, P., Olszak, Z. On almost cosymplectic (−1, μ, 0)-spaces. centr.eur.j.math. 3, 318–330 (2005). https://doi.org/10.2478/BF02479207
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DOI: https://doi.org/10.2478/BF02479207
Keywords
- Almost cosymplectic manifold
- \(\mathcal{D}\)-homothetic transformation
- almost cosymplectic (κ, μ, ν)-space