Contact Spinc Structure, Embeddability of CR Structure, and Positivity of the Mass

摘要：

　　We make a survey on the development in recent years, of positive mass theorem in CR geometry.We study the positive mass problem through a spinor method.So starting with a (contact) spinc structure on the contact bundle over an asymptotically Heisenberg manifold, we have a general Weitzenbock formula.The formula contains a trace curvature term and a T-derivative term besides typical terms as in the Riemannian situation.To deal with the trace curvature term, we may impose a condition like vanishing first Chern class of the canonical line bundle or the existence of contact spinc structure for dimension ≥ 5.To deal with the T-derivative term, we apply a result that the CR Paneitz operator is nonnegative for dimension≥ 5 (in fact, in dimension 5, there is no such term).In dimension 3, the trace curvature term is absorbed in the scalar curvature term for the canonical contact spinc structure while the nonnegativity of the Paneitz term associated to the T-derivative implies the embeddability of the underlying CR structure (and the converse is a conjecture).We obtain a positive mass theorem in dimension 3.We apply it to find solutions of the CR Yamabe problem with minimal energy.

关键词： Spinc structure contact bundle asymptotically Heisenberg manifold ADM-like mass Kohns Laplacian CR Paneitz operator embeddability

作者: Jih-Hsin Cheng

作者单位: INSTITUTE OF MATHEMATICS, ACADEMIA SINICA AND NCTS TAIPEI OFFICE, TAIPEI, TAIWAN, 10617, CHINA

会议类型: 国际会议

会议名称: The 6th International Congress of Chinese Mathematicians (第6届世界华人数学家大会)

会议地点: 台北

会议语种:英文

页码: 23-35

在线出版日期: 2013-07-14（万方平台首次上网日期，不代表论文的发表时间）