Study on Surfaces of the Lorentzian from the viewpoint of singularity theory

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K17548
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Akita National College of Technology
• Principal Investigator: Kasedo Masaki 秋田工業高等専門学校, その他部局等, 准教授 (40705117)
• Research Collaborator: Nabarro Ana Claudia University of San Paulo, ICMC ; Maria Aparecida Soares Ruas University of San Paulo, ICMC
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 特異点論 / 微分幾何学 / ローレンツ幾何学 / 曲面論 / 漸近方向 / 不変式 / 判別式

Outline of Final Research Achievements

We studied space-like surfaces of co-dimension three in de Sitter five space. An asymptotic direction is defined as a kernel direction of a second fundamental form of the space-like surface with respect to a light-like normal direction. A rank two set generically consists of a regular curve. A lifted surfaces has singularities on the rank two set.
If an equation of bi-normal directions has multiple roots, then an equation of the asymptotic directions also has multiple roots. We obtained some invariants that give us some information of a multiplicity of the asymptotic directions.

Free Research Field

微分幾何学