Abstract
Let (Mn, g, e–f dvolg) be a smooth metric measure space of dimension n. In this note, we first prove a nonexistence result for Mn with the Bakry-Émery Ricci tensor is bounded from below. Then we show that f $\in$ L∞ (Mn, e–f dvol) and |∇f| $\in$ L∞ (Mn, e–f dvol) are equivalent for complete gradient shrinking Ricci solitons. Furthermore, we prove that there is no non-Einstein shrinking soliton when the normalized function $\tilde f$ is non-positive.
Citation
Yawei Chu. "Nonexistence of nontrivial quasi-Einstein metrics." Kodai Math. J. 35 (2) 374 - 381, June 2012. https://doi.org/10.2996/kmj/1341401057
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