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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 3, Issue 2

Issues

Volume 13 (2015)

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

Piotr Dacko / Zbigniew Olszak
Published Online: 2005-06-01 | DOI: https://doi.org/10.2478/BF02479207

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.

Keywords: Almost cosymplectic manifold; $$\mathcal{D}$$ -homothetic transformation; almost cosymplectic (κ, μ, ν)-space

Keywords: 53C25; 53D15

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About the article

Published Online: 2005-06-01

Published in Print: 2005-06-01


Citation Information: Open Mathematics, Volume 3, Issue 2, Pages 318–330, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/BF02479207.

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© 2005 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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