Twistor lifts for submanifolds in quaternion Kaehler manifolds and quaternionic complex differential geometry

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540081
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Kanazawa University
• Principal Investigator: HASEGAWA Kazuyuki 金沢大学, 学校教育系, 准教授 (50349825)
• Co-Investigator(Kenkyū-buntansha): MORIYA Katsuhiro 筑波大学, 数理物質科学研究科(系), 助教 (50322011)
• Co-Investigator(Renkei-kenkyūsha): TSUKADA Kazumi お茶の水女子大学, 人間文化創成科学研究科, 教授 (30163760)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: ツイスターリフト / ツイスター空間 / 四元数多様体

Outline of Final Research Achievements

We find some invariants which are independent of the choice of connections preserving the quaternion structure. We study the relations among those invariants and extrinsic quantities for submanifolds, in particular, topological ones. As an application, an inequality for the Euler number of the normal bundle of a twistor holomorphic surface, which is given by T. Friedrich, can be improved. We also study submanifolds in quaternion Kaehler manifolds whose twistor lifts are harmonic sections. As a special case, we see that the twistor lift of a twistor holomorphic surface in a quaternion Kaehler manifold is a harmonic section. It is a generalization of a Leschke's result.

Free Research Field

微分幾何学