Gradient Ricci solitons carrying a closed conformal vector field

2021/10/27 by J. F. Siva Filho, Ramesh Sharma, Filho, J. F. Siva +1
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.2110.14103

Abstract

We show that a complete gradient Ricci soliton (Mⁿ, g) with constant scalar curvature and a non-parallel closed conformal vector field is isometric to either the Euclidean space, or an Euclidean sphere, or negatively Einstein warped product of the real line with a complete non-positively Einstein manifold. Moreover, we show that a Kähler gradient Ricci soliton of real dimension ≥ 4, with a non-parallel closed conformal real vector field is Ricci-flat (Calabi-Yau) and is flat in dimension 4. Finally, we show that a Ricci soliton whose associated 1-form is harmonic, has constant scalar curvature.

Related

• On gradient Ricci solitons with constant scalar curvature
• Compact almost Ricci solitons with constant scalar curvature are gradient
• Some results on η-Ricci Soliton and gradient ρ-Einstein soliton in a complete Riemannian manifold
• On a classification of 4-d gradient Ricci solitons with harmonic Weyl curvature
• Locally Conformally Flat Lorentzian Gradient Ricci Solitons