Ends of shrinking gradient ρ-Einstein solitons

2023/08/14 by Borges, Valter, Rosero-García, Hector, Santos, João Paulo dos · 1 citation
#35Q51 #53C20 #53C21 #53C25 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.07182

Abstract

We prove that all ends of a gradient shrinking ρ-Einstein soliton are φ-non-parabolic, provided ρ is nonnegative and the soliton has bounded and nonnegative scalar curvature, where the weight φ is a negative multiple of the potential function. We also show these solitons are connected at infinity for ρ∈[0,1/2(n-1)), n≥4, and a suitable bound for the scalar curvature.

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• Topology at infinity of complete gradient Schouten solitons

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