Motivated by the work of Li and Mantoulidis [C. Li, C. Mantoulidis, Positive scalar curvature with skeleton singularities, Math. Ann. 374(1–2) (2019) 99–131], we study singular metrics which are uniformly Euclidean [Formula: see text] on a compact manifold ([Formula: text]) negative Yamabe invariant text]. It is well known that if smooth metric unit volume text], then Einstein. We show, in all ...

Abstract The paper is an attempt to resolve the prescribed Chern scalar curvature problem. We look for solutions within conformal class of a fixed Hermitian metric. divide problem in three cases, according sign Gauduchon degree, that we analyse separately. In case where degree negative, prove every non-identically zero and non-positive function unique metric one. Moreover, if there exists balan...

In this paper we prove the existence of Kähler metrics of constant scalar curvature on the blow up at finitely many points of a compact manifold which already carries a Kähler constant scalar curvature metric. Necessary conditions of the number and locations of the blow up points are given. 1991 Math. Subject Classification: 58E11, 32C17.

In this paper, we study Kropina metrics with isotropic scalar curvature. First, obtain the expressions of Ricci curvature tensor and Then, characterize on by analysis.