Differential geometry of complex and almost complex manifolds

• Project/Area Number: 20540057
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Tohoku University
• Principal Investigator: BANDO Shigetoshi Tohoku University, 大学院・理学研究科, 教授 (40165064)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2008: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
• Keywords: 複素多様体 / 概複素多様体 / 局所完備双曲性 / 標準接続 / 安定性 / 正則ベクトル束

Research Abstract

The Kobayashi hyperbolicity is also defined for almost complex manifolds. Though analytical proofs of locally complete hyperbolicity for almost complex manifolds were known, we obtained a new differential geometric one. The moment map of Kaehler manifolds are important since it is involved with the problem of stability. It is extended to the analogous one for almost Kaehler manifolds. We found that it becomes simpler in a sense for the almost Kaehler manifolds, since one does not need the integrability conditions.