Research on rigidity of foliations and group actions based on characteristic classes

2016 Fiscal Year Final Research Report

• Project/Area Number: 26800047
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Ritsumeikan University
• Principal Investigator: Nozawa Hiraku 立命館大学, 理工学部, 准教授 (80706557)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 微分位相幾何 / 葉層構造 / 特性類 / 剛性理論 / 対称空間 / 局所化 / 佐々木幾何

Outline of Final Research Achievements

I investigated on foliations, which are geometric structures on spaces detemined by a decomposition of the space to lower dimensional spaces. The first main result of this project is obtained in a collaboration with G. Meigniez (University of South Bourtagne): We proved that Lie foliations with locally symmetric leaves are homogeneous. We applied this result to prove certain rigidity of Riemannian foliations. The second main result of this project is obtained in a collaboration with O. Goertsches (Marburg University) and D. Toben (Federal University of San Carlos). We showed a Atiyah-Bott-Berline-Vergne type localization formula for characteristic classes of Killing foliations to calculate the volume of Sasakian manifolds. We also obtained some results on characteristic classes of Kahler foliations and certain foliations on the unit tangent bundle of hyperbolic manifolds.

Free Research Field

幾何学