Integrability theorems and conformally constant Chern scalar curvature metrics in almost Hermitian geometry
Abstract
The various scalar curvatures on an almost Hermitian manifold are studied, in particular with respect to conformal variations. We show several integrability theorems, which state that two of these can only agree in the Kähler case. Our main question is the existence of almost Kähler metrics with conformally constant Chern scalar curvature. This problem is completely solved for ruled manifolds and in a complementary case where methods from the ChernYamabe problem are adapted to the nonintegrable case. Also a moment map interpretation of the problem is given, leading to a Futaki invariant and the usual picture from geometric invariant theory.
 Publication:

arXiv eprints
 Pub Date:
 March 2017
 arXiv:
 arXiv:1703.01323
 Bibcode:
 2017arXiv170301323L
 Keywords:

 Mathematics  Differential Geometry;
 53B35;
 53C55
 EPrint:
 26 pages