A Weierstrass type representation for surfaces via loop group method and its applications

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400059
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Hokkaido University
• Principal Investigator: Kobayashi Shimpei 北海道大学, 理学研究院, 准教授 (40408654)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 可積分曲面 / ループ群 / ワイエルシュトラス型の表現公式 / 停留曲面

Outline of Final Research Achievements

Surfaces whose structure equation can be given by an integrable system are often called integrable surfaces. Here the integrable systems is a generic term used to refer to solvable (partial) differential equations. In particular many integrable surfaces have a Weierstrass type representation in terms of loop groups and holomorphic functions.
In this research we studied integrable surfaces by using the Weierstrass type representation. Concretely, we studied affine harmonic maps, constant Gaussian curvature surfaces in 3-dimensional hyperbolic space, discrete affine spheres, affine plane curves and maximal surfaces in 3-dimensional Anti-de Sitter space.

Free Research Field

幾何学