On the symplectic structure deformations related to the Monge–Ampère equation on the Kähler manifold P2(C)

Balinsky, A. A. ORCID: https://orcid.org/0000-0002-8151-4462, Prykarpatski, A. K., Pukach, P. Ya. and Vovk, M. I. 2023. On the symplectic structure deformations related to the Monge–Ampère equation on the Kähler manifold P2(C). Ukrainskyi Matematychnyi Zhurnal 75 (1) 10.37863/umzh.v75i1.7320

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Abstract

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). Based on 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 K\"{a}hler manifold P2(C), that generate Hermitian metrics on it and 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.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Mathematics
ISSN:	1027-3190
Date of First Compliant Deposit:	28 February 2023
Date of Acceptance:	26 December 2022
Last Modified:	10 Apr 2024 09:05
URI:	https://orca.cardiff.ac.uk/id/eprint/157383

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