The construction of canonical form theory in geometry

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400070
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Kyoto Institute of Technology
• Principal Investigator: Ikawa Osamu 京都工芸繊維大学, 基盤科学系, 教授 (60249745)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 対称三対 / 対称空間 / 超極作用 / 実形 / Hermann作用

Outline of Final Research Achievements

(1) For a given compact connected simple Lie group and an involution on it, we can define a hyperpolar action. The author studied the orbit space and the properties of each orbit of the action. The result is a natural extension of maximal torus theory.

(2) We studied the necessary and sufficient condition that two real forms in a Hermitian symmetric space of compact type intersect discretely. When the intersection is discrete we expressed the intersection as the orbit of a Weyl group which is defined by a symmetric triad. Moreover we generalized the result when the ambient space is a generalized flag manifold.

Free Research Field

幾何学