On the symplectic structure deformations related to the Monge–Ampère equation on the Kähler manifold $P_{2}(\mathbb{C})$
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 manifold $P_{2}(\mathbb{C}).$ 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 $P_{2}(\mathbb{C}),$ 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 $P_{2}(\mathbb{C})$ is generalized and the related metric deformations are discussed.
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