双曲 Kenmotsu 流形上的近 Yamabe孤立子

Almost Yamabe Solitons on Hyperbolic Kenmotsu Manifolds

利用 Lie 导数算子,协变微分算子以及共形向量场的性质,证明在具有双曲 Kenmotsu 结构的近 Yamabe 孤立子中, 如果存在光滑函数f,使得切触1−形式η不变,则其势向量场是 Killing 向量场。

By using the properties of Lie-derivative operator, covariant derivative operator and conformal vector field, we prove that in almost Yamabe solitons with hyperbolic Kenmotsu structrue, if there exists a smooth function f that leaves the contact 1-form η invariant, then its potential vector fields are Killing vector fields.