Form-Type Calabi-Yau Equations
Differential Geometry
2010-10-15 v4 Analysis of PDEs
Abstract
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.
Cite
@article{arxiv.0908.0577,
title = {Form-Type Calabi-Yau Equations},
author = {Jixiang Fu and Zhizhang Wang and Damin Wu},
journal= {arXiv preprint arXiv:0908.0577},
year = {2010}
}
Comments
revised version