Flexibility of Reeb flows in contact manifolds

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04837
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Chiba University
• Principal Investigator: Inaba Takashi 千葉大学, 大学院理学研究院, 名誉教授 (40125901)
• Co-Investigator(Renkei-kenkyūsha): TSUBOI Takashi 東京大学, 大学院数理科学研究科, 教授 (40114566) ; MATSUMOTO Shigenori 日本大学, 理工学部, 名誉教授 (30186374) ; MITSUMATSU Yoshihiko 中央大学, 理工学部, 教授 (90206441) ; NAKAYAMA Hiromichi 青山学院大学, 理工学部, 教授 (30227970)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: レーブ流 / 接触構造

Outline of Final Research Achievements

We have studied a method of modifying a Reeb flow by changing a contact form while keeping a contact structure unchanged. We have realized, in a Darboux chart, products of spheres as an invariant set of a Reeb flow. We have also proved the following extension theorem for Reeb flows. Let (M,D) be a compact contact manifold, N a submanifold of M and φ a flow on N. Then, φ extends to a Reeb flow on M if and only if φ preserves the intersection of D and TN. Moreover, if N is isotropic, then, any flow on N transverse to D extends, after a suitable reparametrization, to a Reeb flow.

Free Research Field

数物系科学