Teichmuller space and its topological dynamics via flat singular metrics on a surface

2015 Fiscal Year Final Research Report

• Project/Area Number: 23540103
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Josai University
• Principal Investigator: Nishi Haruko 城西大学, 理学部, 准教授 (90274430)
• Co-Investigator(Renkei-kenkyūsha): OHSHIKA Ken'ichi 大阪大学, 大学院理学研究科, 教授 (70183225) ; KOMORI Yohei 早稲田大学, 教育学部, 教授 (70264794) ; MIYACHI Hideki 大阪大学, 大学院理学研究科, 准教授 (40385480)
• Project Period (FY): 2011-04-28 – 2016-03-31
• Keywords: タイヒミュラー空間 / 錐状特異点 / 平坦計量 / 擬エルミート計量

Outline of Final Research Achievements

We study the geometry of Teichmuller space through the identification with the moduli space of flat metrics on a surface with cone singularities and aim to clarify the properties of its topological dynamics. As a result, we obtain the description of the signature of the area form by the cone angle data in the case of Riemann sphere to show the existence of the family of quasi-Hermite metrics on the moduli space of flat metrics with cone singularities of any positive or negative cone angles.

Free Research Field

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