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A note on generalized quasi‐Einstein manifolds
Author(s) -
Deng YiHua
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400154
Subject(s) - einstein , mathematics , ricci flat manifold , scalar curvature , manifold (fluid mechanics) , constant (computer programming) , pure mathematics , einstein manifold , einstein's constant , dimension (graph theory) , curvature , mathematical physics , mathematical analysis , geometry , mechanical engineering , computer science , engineering , programming language
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 , ρ ) ‐quasi‐Einstein manifolds and prove that these manifolds with dimension four are either Einstein or locally conformally flat under some suitable conditions.