V-static spaces with positive isotropic curvature

2021/03/30 by Gabjin Yun, Yun, Gabjin, Seungsu Hwang +1
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2103.16039

Abstract

In this paper, we give a complete classification of critical metrics of the volume functional on a compact manifold M with boundary ∂ M having positive isotropic curvature. We prove that for a pair (f, κ) of a nontrivial smooth function f: M → \Bbb R and a nonnegative real number κ, if (M, g) having positive isotropic curvature satisfies Ddf - (Δf)g - f\rm Ric = κg, then (M, g) is isometric to a geodesic ball in \Bbb Sⁿ when κ>0, and either M isometric to \Bbb Sⁿ₊, or the product I × \Bbb S^n-1, up to finite cover when κ=0.

Citations

• On Bach-flat gradient shrinking Ricci solitons

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