Contents Online

# Mathematical Research Letters

## Volume 17 (2010)

### Number 5

### Form–type Calabi–Yau equations

Pages: 887 – 903

DOI: http://dx.doi.org/10.4310/MRL.2010.v17.n5.a7

#### Authors

#### Abstract

Motivated from mathematical aspects of the superstring theory, we introduce a new equation on a balanced, hermitian manifold, with zero first Chern class. By 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 Kähler manifold.