Study of Complex Structures and Conformal Geometric Structures on Homogeneous Spaces

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400066
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Niigata University
• Principal Investigator: HASEGAWA KEIZO 新潟大学, 人文社会・教育科学系, 教授 (00208480)
• Co-Investigator(Kenkyū-buntansha): KAMISHIMA YOSHINOBU 城西大学, 理学部, 教授 (10125304) ; TSUKADA KAZUMI お茶の水女子大学, 大学院・人間文化創成科学研究科, 教授 (30163760) ; MORIYA KATSUHIRO 筑波大学, 数理物理科学研究科, 助教 (50322011)
• Co-Investigator(Renkei-kenkyūsha): MABUCHI TOSHIKI 大阪大学, 理学研究科, 名誉教授 (80116102)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 局所共形ケーラー構造 / 等質多様体

Outline of Final Research Achievements

In the field of Complex Geometry "Kaehler structure" is a central subject. As a study of locally conformally Kaehler structures (LCK structure for short) we have shown that a compact homogeneous LCK manifold is a holomorphic fibre bundle over a flag manifold with fiber a 1-complex torus. Furthermore, we have shown that they are all of Vaisman type, that is, its associated Lee form is parallel with respect to the Riemann metric.
As an important research activity during the period of this research project we have organised the international symposium "Complex Geometry and Lie Groups" in Torino, June 16-20, 2015 and in Nara, March 22-26, 2016.

Free Research Field

複素幾何学