On Chern-Yamabe problem
Differential Geometry
2017-09-05 v2
Abstract
We initiate the study of an analogue of the Yamabe problem for complex manifolds. More precisely, fixed a conformal Hermitian structure on a compact complex manifold, we are concerned in the existence of metrics with constant Chern scalar curvature. In this note, we set the problem and we provide a positive answer when the expected constant Chern scalar curvature is non-positive. In particular, this includes the case when the Kodaira dimension of the manifold is non-negative. Finally, we give some remarks on the positive curvature case, showing existence in some special cases and the failure, in general, of uniqueness of the solution.
Cite
@article{arxiv.1501.02638,
title = {On Chern-Yamabe problem},
author = {Daniele Angella and Simone Calamai and Cristiano Spotti},
journal= {arXiv preprint arXiv:1501.02638},
year = {2017}
}