Chern-Yamabe problem and Chern-Yamabe soliton

Abstract

Let [Formula: see text] be a compact complex manifold of complex dimension [Formula: see text] endowed with a Hermitian metric [Formula: see text]. The Chern-Yamabe problem is to find a conformal metric of [Formula: see text] such that its Chern scalar curvature is constant. In this paper, we prove that the solution to the Chern-Yamabe problem is unique under some conditions. On the other hand, we obtain some results related to the Chern-Yamabe soliton.

Prescribed Chern scalar curvatures on compact Hermitian manifolds with negative Gauduchon degree

“…By using geometric flows related to Calamai-Zou's Chern-Yamabe flow, Ho [9] studied the problem of prescribing Chern scalar curvature on balanced Hermitian manifolds with negative Chern scalar curvature. Besides, Ho-Shin [10] showed that the solution to the Chern-Yamabe problem is unique under suitable conditions and obtained some results related to the Chern-Yamabe soliton.…”