Research on surface from singular view point

Research Project

Project/Area Number	24540067
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Multi-year Fund
Section	一般
Research Field	Geometry
Research Institution	Saitama University
Principal Investigator	FUKUI Toshizumi 埼玉大学, 理工学研究科, 教授 (90218892)
Project Period (FY)	2012-04-01 – 2015-03-31
Project Status	Completed (Fiscal Year 2014)
Budget Amount *help	¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000) Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000) Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000) Fiscal Year 2012: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Keywords	特異曲面 / 特異点論 / 距離2乗関数 / 高さ関数 / 特異点 / 国際研究者交流
Outline of Final Research Achievements	We investigate singular surface in the three dimensional euclidean space from singularity theory point of view. We obtain Koendrink type theorem for Whitney umbrella singularities with respect to the singularity type of their plane section. We found the contact of double point locus with the plane come to enjoy. This is an important result since it is the first step to understand the contact of singular surfaces with planes. We also obtain an asymptotic formula of principal curvature and principal direction for weighted cone singularities.

Report

(4 results)