Almost positive curvature on the Gromoll-Meyer sphere

被引：19

作者：

Eschenburg, J. -H. ^{[1
]}

Kerin, M. ^{[2
]}

机构：

[1] Univ Augsburg, Inst Math, D-86135 Augsburg, Germany

[2] Univ Penn, Dept Math, Philadelphia, PA 19104 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2008年 / 136卷 / 09期

关键词：

biquotients; Lie groups; left invariant metrics; quaternions;

D O I：

10.1090/S0002-9939-08-09429-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Gromoll and Meyer have represented a certain exotic 7-sphere Sigma(7) as a biquotient of the Lie group G = Sp( 2). We show for a 2- parameter family of left invariant metrics on G that the induced metric on Sigma(7) has strictly positive sectional curvature at all points outside four subvarieties of codimension >= 1 which we describe explicitly.

引用

页码：3263 / 3270

页数：8

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