On a Class of Gradient Almost Ricci Solitons

2020/01/03 by Güler, Sinem · 1 citation
#53C21 \and 53C50 \and 53C25 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2001.00749

Abstract

In this study, we provide some classifications for half-conformally flat gradient f-almost Ricci solitons, denoted by (M, g, f), in both Lorentzian and neutral signature. First, we prove that if ||∇ f|| is a non-zero constant, then (M, g, f) is locally isometric to a warped product of the form I ×_φ N, where I ⊂ ℝ and N is of constant sectional curvature. On the other hand, if ||∇ f|| = 0, then it is locally a Walker manifold. Then, we construct an example of 4-dimensional steady gradient f-almost Ricci solitons in neutral signature. At the end, we give more physical applications of gradient Ricci solitons endowed with the standard static spacetime metric.

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