On the symplectic structure deformations related to the Monge–Ampère equation on the Kähler manifold<mml:math><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo form="prefix">(</mml:mo><mml:mi>ℂ</mml:mi><mml:mo form="postfix">)</mml:mo></mml:mrow></mml:mrow></mml:math>-Reference-Cited by-同舟云学术

On the symplectic structure deformations related to the Monge–Ampère equation on the Kähler manifoldP2(ℂ)

Published:2023-02-05 Issue:1 Volume:75 Page:28-37
ISSN:1027-3190
Container-title:Ukrains’kyi Matematychnyi Zhurnal
language:
Short-container-title:Ukr. Mat. Zhurn.

Author:

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

Abstract

UDC 517.9 We analyze the cohomology structure of the fundamental two-form deformation related to a modified Monge–Ampère type on the complex Kähler manifoldP2(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 manifoldP2(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 manifoldP2(ℂ)is generalized and the related metric deformations are discussed.

Publisher

SIGMA (Symmetry, Integrability and Geometry: Methods and Application)

Subject

General Earth and Planetary Sciences,General Engineering,General Environmental Science

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