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On the Deformations of Symplectic Structure Related to the Monge–Ampère Equation on the Kähler Manifold P2(ℂ)

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Ukrainian Mathematical Journal Aims and scope

We analyze the cohomology structure of the fundamental two-form deformation related to a modified Monge–Ampère type on the complex Kähler manifold P2(ℂ). On the basis of the Levi-Civita connection and the related vector-field deformation of the fundamental two-form, we construct a hierarchy of bilinear symmetric forms on the tangent bundle of the Kähler manifold P2(ℂ) generating Hermitian metrics on it and the corresponding solutions to the Monge–Ampère-type equation. The classical fundamental two-form construction on the complex Kähler manifold P2(ℂ) is generalized and the related metric deformations are discussed.

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Authors and Affiliations

  1. Mathematics Institute at the Cardiff University, Cardiff, UK

    A. A. Balinsky

  2. Cracow University of Technology, Kraków, Poland

    A. K. Prykarpatski

  3. Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, Lviv, Ukraine

    A. K. Prykarpatski, P. Ya. Pukach & M. I. Vovk

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  1. A. A. Balinsky
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  2. A. K. Prykarpatski
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  3. P. Ya. Pukach
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  4. M. I. Vovk
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Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 1, pp. 28–37, January, 2023. Ukrainian DOI: 10.37863/umzh.v75i1.7320.

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Balinsky, A.A., Prykarpatski, A.K., Pukach, P.Y. et al. On the Deformations of Symplectic Structure Related to the Monge–Ampère Equation on the Kähler Manifold P2(ℂ). Ukr Math J 75, 29–39 (2023). https://doi.org/10.1007/s11253-023-02183-w

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  • DOI: https://doi.org/10.1007/s11253-023-02183-w

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