AI 中文总结
本文研究Yamabe型广义$m$-拟爱因斯坦流形的刚性，证明在自然条件下势向量场要么恒为零要么成为非平凡Killing向量场。
AI 中文摘要
受几乎Yamabe孤子概念的启发，本文研究了一类特殊的广义$m$-拟爱因斯坦流形，我们称之为Yamabe型广义$m$-拟爱因斯坦流形。我们研究了与这些流形相关的势（或定义）向量场在紧致和非紧致情形下的刚性性质。我们证明，在某些自然假设下，势向量场要么恒为零，要么成为非平凡的Killing向量场。
英文摘要
Motivated by the concept of almost Yamabe solitons, a special class of generalized $m$-quasi-Einstein manifolds is investigated in this paper. We refer to these Riemannian manifolds as generalized $m$-quasi-Einstein manifolds of Yamabe-type. We study the rigidity properties for the potential (or defining) vector field associated to these manifolds in both the compact and non-compact settings. We show that under certain natural assumptions the potential vector field either vanishes identically or becomes a non-trivial Killing vector field.
Commentsv2: 14 pages. Comments are most welcome
