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- Title
On the Deformations of Symplectic Structure Related to the Monge–Ampère Equation on the Kähler Manifold P<sub>2</sub>(ℂ).
- Authors
Balinsky, A. A.; Prykarpatski, A. K.; Pukach, P. Ya.; Vovk, M. I.
- 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). 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.
- Subjects
MONGE-Ampere equations; COMPLEX manifolds; TANGENT bundles; DEFORMATIONS (Mechanics); HERMITIAN forms; BILINEAR forms
- Publication
Ukrainian Mathematical Journal, 2023, Vol 75, Issue 1, p29
- ISSN
0041-5995
- Publication type
Article
- DOI
10.1007/s11253-023-02183-w