Rigidity of Einstein manifolds and generalized quasi-Einstein manifolds
Volume 115 / 2015
Annales Polonici Mathematici 115 (2015), 235-240
MSC: Primary 53C25; Secondary 53C21.
DOI: 10.4064/ap115-3-3
Abstract
We discuss the rigidity of Einstein manifolds and generalized quasi-Einstein manifolds. We improve a pinching condition used in a theorem on the rigidity of compact Einstein manifolds. Under an additional condition, we confirm a conjecture on the rigidity of compact Einstein manifolds. In addition, we prove that every closed generalized quasi-Einstein manifold is an Einstein manifold provided $\mu =-{1/(n-2)}$, $\lambda \leq 0$ and $\beta \leq 0$.
