On the symplectic structure deformations related to the Monge–Ampère equation on the Kähler manifold P2(C)
DOI:
https://doi.org/10.37863/umzh.v75i1.7320Keywords:
Kähler manifold, symplectic deformation, Levi–Civita connection, metric deformation, Monge–Ampère equationAbstract
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 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.
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