一类特殊的拟几乎Einstein度量直径的下界估计

华东师范大学学报(自然科学版) ›› 2014, Vol. 2014 ›› Issue (1): 27-35.

一类特殊的拟几乎Einstein度量直径的下界估计

胡玲娟, 毛晶晶, 王林峰

南通大学~~理学院,\; 江苏~南通\; 226007

收稿日期:2013-03-01 修回日期:2013-06-01 出版日期:2014-01-25 发布日期:2015-09-25

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

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

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

摘要/Abstract

摘要： 加权~Myer~型定理给出了具有带正下界的~$\tau$-Bakry-\'{E}mery~曲率的完备黎曼流形直径的上界估计,
紧致流形直径的下界估计也是有趣的问题.
本文首先运用~Hopf~极大值原理证明了一类特殊的~$\tau$-拟几乎~Einstein~度量势函数的梯度估计.
运用该梯度估计得到了该度量直径的下界估计.
该结果推广了王林峰的关于紧致~$\tau$-拟~Einstein~度量直径下界估计的结果.

关键词: 拟几乎~Einstein~度量, 梯度估计, 直径估计

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
metrics.

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

中图分类号:

O186

胡玲娟, 毛晶晶, 王林峰. 一类特殊的拟几乎Einstein度量直径的下界估计[J]. 华东师范大学学报(自然科学版), 2014, 2014(1): 27-35.

HU Ling-juan, MAO Jing-jing, WANG Lin-feng. Lower diameter estimate for a special quasi-almost-Einstein metric[J]. Journal of East China Normal University(Natural Sc, 2014, 2014(1): 27-35.

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