Kähler Gradient Ricci Solitons with Large Symmetry

2023/06/09 by Hung Tran, Tran, Hung · 2 citations
Mathematics · Medicine · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Bone health and treatments

paper · pdf · doi:10.48550/arxiv.2306.05787

Abstract

Let (M, g, J, f) be an irreducible non-trivial Kähler gradient Ricci soliton of real dimension 2n. We show that its group of isometries is of dimension at most n² and the case of equality is characterized. As a consequence, our framework shows the uniqueness of U(n)-invariant Kähler gradient Ricci solitons constructed earlier. There are corollaries regarding the groups of automorphisms or affine transformations and a general version for almost Hermitian GRS. The approach is based on a connection to the geometry of an almost contact metric structure.

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• Gradient Shrinking Ricci Solitons and Modified Sectional Curvature
• On Ricci Solitons with Isoparametric Potential Functions

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