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Vanishing bach-like tensors on complete gradient shrinking ricci solitons

2023/07/04 by James Siene, Siene, James
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2307.01882

openalex publication_date 2023/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Bach tensor is classically defined in dimension 4, and work from J. Bergman \citebergman:2004 and others shows that B = (1)/(2)U + (1)/(6)V where U and V are more basic 2-tensors, which are symmetric, divergence-free, algebraically independent, and quadratic in the Riemann tensor. In this paper, we extend H.-D. Cao and Q. Chen's results \citecaochen:2013 for Bach-flat gradient shrinking Ricci solitons to solitons with \mathfrakB = αU + βV = 0.

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