Revisiting Gradient Bach Solitons via Maximum Principles

Authors : Antonio W. Cunha, Eudes L. De Lima, Henrique F. De Lima

Pages : 207-2012

Doi:10.36890/iejg.1466314

View : 39 | Download : 99

Publication Date : 2024-04-23

Article Type : Research Paper

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