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

Autor:	Balinsky, A. A., Prykarpatski, A. K., Pukach, P. Ya., Vovk, M. I.
Předmět:	MONGE-Ampere equations COMPLEX manifolds TANGENT bundles DEFORMATIONS (Mechanics) HERMITIAN forms BILINEAR forms
Zdroj:	Ukrainian Mathematical Journal; Jun2023, Vol. 75 Issue 1, p29-39, 11p
Abstrakt:	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. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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