Cross ratio and its falks

• Project/Area Number: 26400065
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: The University of Tokyo
• Principal Investigator: KANAI Masahiko 東京大学, 大学院数理科学研究科, 教授 (70183035)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2015: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000); Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 複比 / パラケーラー構造 / シュワルツ微分 / 群作用 / 剛性 / 局所剛性 / 構造安定性 / 双曲力学系

Outline of Final Research Achievements

The history of cross ratio goes back to ancient Greece. Nevertheless, our understanding on it or its "falks", namely, Schwarzian derivative, para-Kaehler structures and geodesic currents seems quite restrictive. The present research aimed at improve our understanding on them. In particular, starting from para-Kaehler geometry, we discovered new definitions of to the energy of legandrian knots and of the Gauss maps of hypersurfaces of the hyperbolic space. We are going to develop new theories on those new objects in a year or two.

Research Products

• [Presentation] 力学系の剛性と不変幾何構造 (2016)
  • Author(s): 金井雅彦
  • Organizer: 関東若手幾何セミナー
  • Place of Presentation: 東京大学
  • Year and Date: 2016-01-30
  • Invited
• [Presentation] The cross ratio and its falks (2015)
  • Author(s): Masahiko KANAI
  • Organizer: Geometric Analysis in Geometry and Topology
  • Place of Presentation: Tokyo University of Science
  • Year and Date: 2015-11-09
  • Int'l Joint Research / Invited