THE NONEXISTENCE OF QUASI-EINSTEIN METRICS

被引：68

作者：

Case, Jeffrey S. ^{[1
]}

机构：

[1] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2010年 / 248卷 / 02期

关键词：

Einstein; warped product; quasi-Einstein; RICCI SOLITONS; SCALAR CURVATURE; MANIFOLDS; EXAMPLES;

D O I：

10.2140/pjm.2010.248.277

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study complete Riemannian manifolds satisfying the equation Ric+del(2)f - 1/mdf circle times df = 0 by studying the associated PDE Delta(f)f + m mu exp(2f/m) = 0 for mu <= 0. By developing a gradient estimate for f, we show there are no nonconstant solutions. We then apply this to show that there are no nontrivial Ricci flat warped products with fibers that have nonpositive Einstein constant. We also show that for nontrivial steady gradient Ricci solitons, the quantity R + vertical bar del f vertical bar(2) is a positive constant.

引用

页码：277 / 284

页数：8

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