On the structure of gradient Yamabe solitons

Abstract

We show that every complete nontrivial gradient Yamabe soliton admits a special global warped product structure with a one-dimensional base. Based on this, we prove a general classification theorem for complete nontrivial locally conformally flat gradient Yamabe solitons.

8 pages; added Remark 2.2 and updated references

References in corpus (4)

• On Bach-flat gradient shrinking Ricci solitons
• Bach-flat gradient steady Ricci solitons
• The classification of locally conformally flat Yamabe solitons
• Gradient Yamabe Solitons on Warped Products

Cited by in corpus (3)

• Conformal Yamabe soliton and $\ast$-Yamabe soliton with torse forming potential vector field
• Exact decay rate of a nonlinear elliptic equation related to the Yamabe flow
• A Note On Andrews Inequality