W. Costa-Filho

Integral Identities and Rigidity of Generalized $m$-Quasi-Einstein Manifolds

We prove that every closed $m$-quasi-Einstein manifold $(M^n,g,X,\lambda)$ with constant $\lambda\leq0$ is trivial whenever $m\leq-2$. This establishes the Colling--Dunajski conjecture in the range $m\leq-2$ and, for $n\geq5$, extends the previously known range $m\leq2-n$. This result is placed within a broader study o...