Some triviality characterizations on gradient almost Yamabe solitons. (English) Zbl 1534.53040
Summary: An almost Yamabe soliton is a generalization of the Yamabe soliton. In this article, we deduce some results regarding almost gradient Yamabe solitons. More specifically, we show that a compact almost gradient Yamabe soliton having non-negative Ricci curvature is trivial. Again, we prove that an almost gradient Yamabe soliton with a non-negative potential function and scalar curvature bound admitting an integral condition is trivial. Moreover, we give a characterization of a compact almost gradient Yamabe solitons.
MSC:
| 53C20 | Global Riemannian geometry, including pinching |
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
| 53E20 | Ricci flows |
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