The Sasaki join and admissible Kahler constructions

JOURNAL OF GEOMETRY AND PHYSICS

卷:91

Article

Boyer, Charles P.¹  Tonfiesen-Friedman, Christina W.² 

[1] Univ New Mexico, Dept Math & Stat, Albuquerque, NM 87131 USA

[2] Union Coll, Dept Math, Schenectady, NY 12308 USA

关键词: Extremal Sasakian metrics;    Extremal Kahler metrics;    Constant scalar curvature;    Join construction;   

DOI  :  10.1016/j.geomphys.2014.10.002

来源: Elsevier

【 摘 要 】

We give a survey of our recent work (Boyer and Tonnesen-Friedman (2013) [50,51,30], Boyer and Tonnesen-Friedman (2014) [33,29,36]) describing a method which combines the Sasaki join construction of Boyer et al. (2007) [31] with the admissible Miller construction of Apostolov et al. (2006, 2004, 2008) [26,27,14,25] to obtain hew extremal and new constant scalar curvature Sasaki metrics, including Sasaki-Einstein metrics. The constant scalar curvature Sasaki metrics also provide explicit solutions to the CR Yamabe problem. In this regard we give examples of the lack of uniqueness when the Yamabe invariant lambda(M) is positive. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free