Form-Type Calabi-Yau Equations

Details Form-Type Calabi-Yau Equations Form-Type Calabi-Yau Equations

2009-08-05

arxiv.org/abs/0908.0577v4

Math. Res. Lett. 17(2010), 887-903

Mathematics

Differential Geometry

revised version

Scientific paper

Motivated from mathematical aspects of the superstring theory, we introduce a new equation on a balanced, hermitian manifold, with zero first Chern class. Solving the equation, one will obtain, in each Bott--Chern cohomology class, a balanced metric which is hermitian Ricci--flat. This can be viewed as a differential form level generalization of the classical Calabi--Yau equation. We establish the existence and uniqueness of the equation on complex tori, and prove certain uniqueness and openness on a general K\"ahler manifold.

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