论文标题
刚度施顿孤子的刚度结果
Rigidity results on gradient Schouten solitons
论文作者
论文摘要
In this paper we consider $ρ$-Einstein solitons of type $M= \left(B^n, g^{*}\right) \times (F^m,g_F)$, where $\left(B^n,g^{*}\right)$ is conformal to a pseudo-Euclidean space and invariant under the action of the pseudo-orthogonal group, and $ \ left（f^m，g_ {f} \ right）$是爱因斯坦歧管。我们为Schouten Soliton案例提供所有解决方案。此外，在Riemannian案件中，我们证明了 $ m = \ left（b^n，g^{*} \ right）\ times（f^m，g_f）$是一个完整的渐变schouten soliton，然后$ \ left（b^{n}，g^{*}} \ right）$是等于$ \ s} n-1} $ restric，紧凑的爱因斯坦歧管。
In this paper we consider $ρ$-Einstein solitons of type $M= \left(B^n, g^{*}\right) \times (F^m,g_F)$, where $\left(B^n,g^{*}\right)$ is conformal to a pseudo-Euclidean space and invariant under the action of the pseudo-orthogonal group, and $\left(F^m,g_{F}\right)$ is an Einstein manifold. We provide all the solutions for the gradient Schouten soliton case. Moreover, in the Riemannian case, we prove that if $M= \left(B^n, g^{*}\right) \times (F^m,g_F)$ is a complete gradient Schouten soliton then $\left(B^{n},g^{*}\right)$ is isometric to $\mathbb{S}^{n-1}\times \mathbb{R}$ and $F^m$ is a compact Einstein manifold.
