• Corpus ID: 252568223

The prescribed Gauduchon scalar curvature problem in almost Hermitian geometry

  title={The prescribed Gauduchon scalar curvature problem in almost Hermitian geometry},
  author={Yuxuan Li and Wubin Zhou and Xianchao Zhou},
. In this paper we consider the prescribed Gauduchon scalar curvature problem on almost Hermitian manifolds. By deducing the expression of the Gauduchon scalar curvature under the conformal variation, the problem is reduced to solve a semi-linear partial differential equation with exponential nonlinearity. Using super and sub-solution method, we show that the existence of the solution to this semi-linear equation depends on the sign of a constant associated to Gauduchon degree. When the sign is… 



The Prescribed Chern Scalar Curvature Problem

  • Elia Fusi
  • Mathematics
    The Journal of Geometric Analysis
  • 2022
The paper is an attempt to resolve the prescribed Chern scalar curvature problem. We look for solutions within the conformal class of a fixed Hermitian metric. We divide the problem in three cases,

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On an almost Hermitian manifold, there are two Hermitian scalar curvatures associated with a canonical Hermitian connection. In this paper, two explicit formulas on these two scalar curvatures are

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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

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. In this paper, we investigate the problem of prescribing Chern scalar curvatures on compact Hermitian manifolds with negative Gauduchon degree. By studying the convergence of the associated

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. We study two natural problems concerning the scalar and the Ricci curvatures of the Bismut connection. Firstly, we study an analog of the Yamabe problem for Hermitian manifolds related to the

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AbstractThe conformal class of a Hermitian metric g on a compact almost complex manifold (M2m, J) consists entirely of metrics that are Hermitian with respect to J. For each one of these metrics, we

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The basic problem posed in [12] is that of describing the set of Gaussian curvature functions which a given 2-dimensional manifold M can possess. In this paper we consider this problem for the case

Characteristic Classes of Hermitian Manifolds

In recent years the works of Stiefel,1 Whitney,2 Pontrjagin,3 Steenrod,4 Feldbau,5 Ehresmann,6 etc. have added considerably to our knowledge of the topology of manifolds with a differentiable