The geometry and asymptotic analysis of hyper-Kaehler manifolds

2015 Fiscal Year Final Research Report

• Project/Area Number: 26887031
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Keio University
• Principal Investigator: Hattori Kota 慶應義塾大学, 理工学部, 講師 (30586087)
• Project Period (FY): 2014-08-29 – 2016-03-31
• Keywords: 超ケーラー多様体 / 接錐 / 特殊ラグランジュ部分多様体 / リッチ曲率 / 距離空間

Outline of Final Research Achievements

(1) I have developed the new construction of compact special Lagrangian submanifolds embedded in toric Hyper-Kaehler manifolds applying Joyce's desingularization. The special Lagrangian submanifolds are the generalization of area minimizing surfaces to the higher dimension. To construct such submanifolds, we have to solve partial differential equations in general. However, I have shown that we can reduce the problem to the argument of elementary linear algebra under the appropriate circumstances.
(2) The Ricci-flat manifolds are the solutions of Einstein's equations in the vacuum. I have constructed the 4 dimensional Ricci-flat manifolds whose asymptotic cones are not unique.

Free Research Field

微分幾何学