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2017 Fiscal Year Final Research Report

Flexibility of Reeb flows in contact manifolds

Research Project

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Project/Area Number 15K04837
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionChiba 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

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Published: 2019-03-29  

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