The critical point equation on a three-dimensional compact manifold
The critical point equation on a three-dimensional compact manifold
On a compact $n$-dimensional manifold $M^n$, a critical point of the total scalar curvature functional, restricted to the space of metrics with constant scalar curvature of volume 1, satisfies the critical point equation (CPE), given by $z_g=sâ^*_g(f)$. It has been conjectured that a solution $(g,f)$ of the CPE is Einstein. …