论文标题
爱因斯坦型结构，贝塞的猜想和$φ$ -cpe公制的独特性结果
Einstein-type structures, Besse's conjecture and a uniqueness result for a $φ$-CPE metric in its conformal class
论文作者
论文摘要
在本文中，我们研究了CPE猜想的扩展，以将$ m $折叠起来，该$ m $支持将曲率与光滑地图$φ的几何形状相关的结构：m \至n $。从变分的角度来看，由$（φ-\ mathrm {cpe}）$表示的结果系统是自然的，并描述了集成的$φ$ -SCALAR曲率函数的固定点，该功能限制为具有单位量和常数$φ$ -Scalar曲率的指标。我们证明了在共同类中$（φ-\ mathrm {cpe}）$的解决方案的刚度语句，又是一个差距定理，在支持$（$ \ mathrm {cpe}）$的流形中表征了圆形球体，并带有$φ$的$ umonic映射。
In this paper, we study an extension of the CPE conjecture to manifolds $M$ which support a structure relating curvature to the geometry of a smooth map $φ: M \to N$. The resulting system, denoted by $(φ-\mathrm{CPE})$, is natural from the variational viewpoint and describes stationary points for the integrated $φ$-scalar curvature functional restricted to metrics with unit volume and constant $φ$-scalar curvature. We prove both a rigidity statement for solutions to $(φ-\mathrm{CPE})$ in a conformal class, and a gap theorem characterizing the round sphere among manifolds supporting $(φ-\mathrm{CPE})$ with $φ$ a harmonic map.
