Integrated research of Calabi-Yau structures and generalized complex structures

2017 Fiscal Year Final Research Report

• Project/Area Number: 25287011
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Osaka University
• Principal Investigator: Goto Ryushi 大阪大学, 理学研究科, 教授 (30252571)
• Co-Investigator(Kenkyū-buntansha): 小木曽 啓示 東京大学, 数理(科)学研究科(研究院), 教授 (40224133) ; 満渕 俊樹 大阪大学, その他部局等, 名誉教授 (80116102) ; 松本 佳彦 大阪大学, 理学(系)研究科(研究院), 助教 (00710625)
• Project Period (FY): 2013-04-01 – 2018-03-31
• Keywords: 一般化された複素構造 / カラビーヤオ構造 / 一般化されたケーラー構造 / ポアソン構造 / 変形理論 / ケーラーアインシュタイン計量 / エルミートアインシュタイン計量 / モーメント写像

Outline of Final Research Achievements

From a view point of the moment map, we introduce the notion of Einstein-Hermitian generalized connections over a generalized Kahler manifold of symplectic type. We show that moduli spaces of Einstein- Hermitian generalized connections arise as the Kahler quotients. The deformation complex of Einstein-Hermitian generalized connections is an elliptic complex and it turns out that the smooth part of the moduli space is a finite dimensional Kahler manifold. The canonical line bundle over a generalized Kahler manifold of symplectic type has the canonical generalized connection and its curvature coincides with ”the scalar curvature as the moment map”. Kahler-Ricci solitons provide examples of Einstein-Hermitian generalized connections and Einstein Hermitian co-Higgs bundles are also discussed.

Free Research Field

微分幾何、複素幾何