On generalized m-quasi-Einstein manifolds with constant Ricci curvatures

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• 作者：Zejun Hu ; ^{huzj@zzu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Dehe Li ^{lidehehe@163.com" class="auth_mail" title="E-mail the corresponding author} ; Shujie Zhai ^{zhaishujie@zzu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Generalized m-quasi-Einstein ; Einstein manifold ; Ricci curvature ; Bakry&ndash ; Emery Ricci tensor ; Homogeneous manifold
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：446
• 期：1
• 页码：843-851
• 全文大小：299 K

文摘

In this paper, we study generalized m  -quasi-Einstein manifold with constant Ricci curvatures. In particular, as the main result we show that for m≠1$m\ne 1$ a proper generalized m  -quasi-Einstein manifold with constant Ricci curvatures is Einstein. Consequently for m≠1$m\ne 1$ every homogeneous proper generalized m-quasi-Einstein manifold must be Einstein.