Stability under deformations of Hermite-Einstein almost-Kähler metrics
Abstract
On a 4-dimensional compact symplectic manifold, we consider a smooth family of compatible almost-complex structures such that at time zero the induced metric is Hermite-Einstein almost-Kähler metric with zero or negative Hermitian scalar curvature. We prove, under certain hypothesis, the existence of a smooth family of compatible almost-complex structures, diffeomorphic at each time to the initial family, and inducing constant Hermitian scalar curvature metrics.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2012
- DOI:
- 10.48550/arXiv.1204.5438
- arXiv:
- arXiv:1204.5438
- Bibcode:
- 2012arXiv1204.5438L
- Keywords:
-
- Mathematics - Differential Geometry;
- 53C25
- E-Print:
- 10 pages. To appear at Annales de l'Institut Fourier. Improved version