Journal of East China Normal University(Natural Sc ›› 2014, Vol. 2014 ›› Issue (1): 27-35.

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Lower diameter estimate for a special quasi-almost-Einstein metric

HU Ling-juan,  MAO Jing-jing,  WANG Lin-feng   

  1. School of Science, Nantong University, Nantong, Jiangsu 226007, China
  • Received:2013-03-01 Revised:2013-06-01 Online:2014-01-25 Published:2015-09-25

Abstract: The weighted Myers' theorem gives an upper bound estimate
for the diameter of a complete Riemannian manifold with the
$\tau$-Bakry-\'{E}mery curvature bounded from below by a positive
number. The lower bound estimate for the diameter of a compact
manifold is also an interesting question. In this paper, a gradient
estimate for the potential function of a special
$\tau$-quasi-almost-Einstein metric was established by using the
Hopf's maximum principle. Based on it, a lower bound estimate for
the diameter of this metric was derived. The result generalizes
Wang's lower diameter estimate for compact $\tau$-quasi-Einstein

Key words: quasi-almost-Einstein metric, gradient estimate, diameter estimate

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