Research on special Lagrangian submanifolds in non-flat Calabi-Yau manifolds

2014 Fiscal Year Final Research Report

• Project/Area Number: 23740057
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Tokyo Metropolitan University
• Principal Investigator: SAKAI Takashi 首都大学東京, 理工学研究科, 准教授 (30381445)
• Project Period (FY): 2011 – 2014
• Keywords: 微分幾何 / 対称空間 / Calabi-Yau多様体 / Lagrange部分多様体 / キャリブレーション / 複素旗多様体 / 対蹠集合

Outline of Final Research Achievements

We studied special Lagrangian submanifolds in Calabi-Yau manifolds. Moreover we investigated Floer homology and Hamiltonian volume minimizing properties of Lagrangian submanifolds, and we also investigated conical singularities on minimal submanifolds.
The cotangent bundles of compact rank one symmetric spaces admit complete Ricci flat Kahler metrics of cohomogeneity one due to M. Stenzel. Using the symmetry of the Stenzel metric, we constructed cohomogeneity one special Lagrangian submanifolds in the cotangent bundle of the sphere by the moment map technique. Furthermore, we observed singularities and the asymptotic behavior of those special Lagrangian submanifolds.

Free Research Field

微分幾何学