Analmost p-Kahler manifold is a triple (M, J, Omega), where (M, J) is an almost complex manifold of real dimension 2n and Omega is a closed real transverse (p, p)-form on (M, J), where 1 <= p <= n. When J is integrable, almost p-Kahler manifolds are called p-Kahler manifolds. We produce families of almost p-Kahler structures (J(t), Omega(t)) on C-3, C-4, and on the real torus T-6, arising as deformations of Kahler structures (J(0), g(0), omega(0)), such that the almost complex structures Jt cannot be locally compatible with any symplectic form for t not equal 0. Furthermore, examples of special compact nilmanifolds with and without almost p-Kahler structures are presented.
Families of Almost Complex Structures and Transverse (p, p)-Forms / Hind, R; Medori, C; Tomassini, A. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 33:10(2023). [10.1007/s12220-023-01391-x]
Families of Almost Complex Structures and Transverse (p, p)-Forms
Medori, C;Tomassini, A
2023-01-01
Abstract
Analmost p-Kahler manifold is a triple (M, J, Omega), where (M, J) is an almost complex manifold of real dimension 2n and Omega is a closed real transverse (p, p)-form on (M, J), where 1 <= p <= n. When J is integrable, almost p-Kahler manifolds are called p-Kahler manifolds. We produce families of almost p-Kahler structures (J(t), Omega(t)) on C-3, C-4, and on the real torus T-6, arising as deformations of Kahler structures (J(0), g(0), omega(0)), such that the almost complex structures Jt cannot be locally compatible with any symplectic form for t not equal 0. Furthermore, examples of special compact nilmanifolds with and without almost p-Kahler structures are presented.File | Dimensione | Formato | |
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