تقرير
The Sasaki Cone and Extremal Sasakian Metrics
| العنوان: | The Sasaki Cone and Extremal Sasakian Metrics |
|---|---|
| المؤلفون: | Boyer, Charles P., Galicki, Krzysztof, Simanca, Santiago R. |
| المصدر: | Proceedings of the Conference on Riemannian Topology, pg 263-290, K. Galicki & S. Simanca, Eds, Birkhauser, Boston, 2008. |
| سنة النشر: | 2007 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, 53C25 |
| الوصف: | We study the Sasaki cone of a CR structure of Sasaki type on a given closed manifold. We introduce an energy functional over the cone, and use its critical points to single out the strongly extremal Reeb vectors fields. Should one such vector field be a member of the extremal set, the scalar curvature of a Sasaki extremal metric representing it would have the smallest $L^2$-norm among all Sasakian metrics of fixed volume that can represent vector fields in the cone. We use links of isolated hypersurface singularities to produce examples of manifolds of Sasaki type, many of these in dimension five, whose Sasaki cone coincides with the extremal set, and examples where the extremal set is empty. We end up by proving that a conjecture of Orlik concerning the torsion of the homology groups of these links holds in the five dimensional case. Comment: 24 pages, to appear in the Proceedings of the Conference on Riemannian Topology, K. Galicki and S.R. Simanca Eds., Birkhauser, Boston |
| نوع الوثيقة: | Working Paper |
| الوصول الحر: | http://arxiv.org/abs/0801.0217Test |
| رقم الانضمام: | edsarx.0801.0217 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |