Topology at infinity of complete gradient Schouten solitons

2023/10/06 by V. Borges, Borges, Valter, H. A. Rosero-García +3 · 1 voice
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · doi:10.1007/s13163-025-00558-0

crossref issued 2025/12/01 · crossref published 2025/12/01 · crossref published-online 2025/12/01 · openalex created_date 2025/12/01 · openalex publication_date 2025/12/01 · crossref created 2025/12/01 · crossref deposited 2025/12/01 · crossref indexed 2026/02/11 · openalex updated_date 2026/07/23

Abstract

In this paper, we study ends of complete gradient non-trivial Schouten solitons. Without any additional assumptions, we show the shrinking ones have finitely many ends, and the expanding ones are connected at infinity. We also provide information regarding the non-parabolicity of the ends in the shrinking setting, and on the behavior of the potential function and volume growth in the expanding case.

Citations

• Geometry of shrinking Ricci solitons
• Rigidity of gradient Einstein shrinkers
• On complete gradient Schouten solitons
• Ends of shrinking gradient ρ-Einstein solitons
• Hamilton-Ivey estimates for the Ricci-Bourguignon flow with ρ<0
• Topology of Kahler Ricci solitons
• Almost soliton duality
• Geometry of manifolds with densities
• Gradient Einstein solitons
• Analysis of weighted Laplacian and applications to Ricci solitons
• Smooth metric measure spaces with non-negative curvature
• Almost-Schur lemma
• On gradient Ricci solitons
• Complete gradient shrinking Ricci solitons have finite topological type
• Comparison Geometry for the Bakry-Emery Ricci Tensor
• Weighted Poincaré inequality and rigidity of complete manifolds

Discussions

• Let $(M^n,g)$ , $n\geq 4$ , be a complete Riemannian manifold. A gradient Schouten soliton is a pair $(g,f)$ satisfying $$ \operatorname{Ric}+\nabla^2 f = \left(\frac{R}{2(n-1)}+\lambda\right)g, $$ wh [stackexchange, 2 points]

Related

• Ends of shrinking gradient ρ-Einstein solitons
• Topology of Kahler Ricci solitons
• Structure at infinity for shrinking Ricci solitons
• Geometry and Topology of Gradient Shrinking Sasaki-Ricci Solitons
• Structure at infinity of expanding gradient Ricci soliton