Revisiting Gradient Bach Solitons via Maximum Principles

Year 2024, Volume: 17 Issue: 1, 207 - 2012, 23.04.2024

Antonio W. Cunha Eudes L. De Lima Henrique F. De Lima

https://doi.org/10.36890/iejg.1466314

Abstract

Supposing that the Ricci curvature has an appropriate lower bound and applying suitable maximum principles, we establish triviality results which guarantee that a gradient Bach soliton must be trivial and Bach-flat. Our approach is based on three main cores: convergence to zero at infinity, polynomial volume growth (both related to complete noncompact Riemannian manifolds) and stochastic completeness.

Keywords

Gradient Bach solitons, triviality, Bach-flat, convergence at infinity, polynomial volume growth, stochastic completeness

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