A note on generalized quasi-Einstein manifolds

作者：Deng; YiHua

来源：Mathematische Nachrichten, 2015, 288(10): 1122-1126.

DOI：10.1002/mana.201400154

• Generalized quasi-Einstein manifolds
• Weyl tensor
• anti-self-dual manifolds
• Einstein manifold

In this note, we get a necessary and sufficient condition such that the scalar curvature of generalized m-quasi-Einstein manifold with m = 1 is constant. In particular, we discuss a class of generalized quasi-Einstein manifolds which are more general than (m, rho)-quasi-Einstein manifolds and prove that these manifolds with dimension four are either Einstein or locally conformally flat under some suitable conditions.

• 出版日期2015-7
• 单位衡阳师范学院