2016/12/29 by Gabjin Yun, Yun, Gabjin, Seungsu Hwang +1
Mathematics · Medicine · #53C25 #58E11 #Advanced Algebra and Geometry #Advanced Neuroimaging Techniques and Applications #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.1612.09125
openalex publication_date 2016/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
On a compact n-dimensional manifold, it is well known that a critical metric of the total scalar curvature, restricted to the space of metrics with unit volume is Einstein. It has been conjectured that a critical metric of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, will be Einstein. This conjecture was proposed in 1987 by Besse, but has yet to be proved. In this paper, we prove the Besse conjecture with a weaker condition than harmonic curvature for n≥ 3.