Fully nonlinear equations on Riemannian manifolds with negative curvature

被引：71

作者：

Gursky, MJ ^{[1
]}

Viaclovsky, JA

机构：

[1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

[2] MIT, Dept Math, Cambridge, MA 02139 USA

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2003年 / 52卷 / 02期

关键词：

fully nonlinear equations; Ricci curvature;

D O I：

10.1512/iumj.2003.52.2313

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is proved that every compact Riemannian manifold of dimension n greater than or equal to 3 with negative Ricci curvature is conformal to a metric with det(Ric) = constant. This is a special case of a more general theorem involving symmetric functions of the eigenvalues of the Ricci tensor.

引用

页码：399 / 419

页数：21

共 18 条

[1]

[Anonymous], 1997, PRINCETON LANDMARKS

[2] Prescribed scalar curvature on compact Riemann varieties in the negative case [J].