The Sasakian Geometry of the Heisenberg Group

被引：0
作者：
Boyer, Charles P. [1 ]
机构：
[1] Univ New Mexico, Dept Math & Stat, Albuquerque, NM 87131 USA
来源：
BULLETIN MATHEMATIQUE DE LA SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE | 2009年 / 52卷 / 03期
关键词：
Heisenberg group; CR structures; Sasaki cone; extremal metrics; CR; MANIFOLDS;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this note I study the Sasakian geometry associated to the standard CR structure on the Heisenberg group, and prove that the Sasaki cone coincides with the set of extremal Sasakian structures. Moreover, the scalar curvature of these extremal metrics is constant if and only if the metric has Phi-sectional curvature -3. I also briefly discuss some relations with the well-know sub-Riemannian geometry of the Heisenberg group as well as the standard Sasakian structure induced on compact quotients.
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页码：251 / 262
页数：12
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