Geodesic
Rigidity of Einstein manifolds and generalized quasi-Einstein manifolds
Yi Hua Deng1 ; Li Ping Luo1 ; Li Jun Zhou1
1College of Mathematics and Statistics Hengyang Normal University Hengyang, Hunan 421002, China
Annales Polonici Mathematici, Tome 115 (2015) no. 3, pp. 235-240
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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 $\beta \leq 0$.
DOI : 10.4064/ap115-3-3
Keywords: discuss rigidity einstein manifolds generalized quasi einstein manifolds improve pinching condition theorem rigidity compact einstein manifolds under additional condition confirm conjecture rigidity compact einstein manifolds addition prove every closed generalized quasi einstein manifold einstein manifold provided n lambda leq beta leq

Yi Hua Deng  1   ; Li Ping Luo  1   ; Li Jun Zhou  1

1 College of Mathematics and Statistics Hengyang Normal University Hengyang, Hunan 421002, China 
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Yi Hua Deng; Li Ping Luo; Li Jun Zhou. Rigidity of Einstein manifolds
 and generalized quasi-Einstein manifolds. Annales Polonici Mathematici, Tome 115 (2015) no. 3, pp. 235-240. doi: 10.4064/ap115-3-3

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