Canonical Kahler metrics, algebro-geometric stability and Sasakian geometry

2016 Fiscal Year Final Research Report

• Project/Area Number: 24540098
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Saitama University (2013-2016); Tokyo University of Science (2012)
• Principal Investigator: ONO Hajime 埼玉大学, 理工学研究科, 准教授 (70467033)
• Co-Investigator(Renkei-kenkyūsha): FUTAKI Akito 東京大学, 大学院数理科学研究科, 教授 (90143247)
• Project Period (FY): 2012-04-01 – 2017-03-31
• Keywords: トーリック幾何 / チャウ安定性 / K-安定性 / ハミルトン体積最小性 / ラグランジュ部分多様体 / 共形ケーラーアインシュタイン・マックスウェル計量

Outline of Final Research Achievements

Based on a viewpoint of “volume minimization property”, we improved knowledge on the following topics for toric Kahler manifolds: algebraic geometry (GIT stability and K-stability), submanifold theory (Hamiltonian volume minimization problem of Lagrangian submanifolds) and existence problem of canonical metrics (Futaki type invariants on conformally Kahler Einstein-Maxwell metrics).

Free Research Field

微分幾何学