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

Research Project

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
Project Status	Completed (Fiscal Year 2017)
Budget Amount *help	¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000) Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000) Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000) Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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 / 特異点
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.