2006 Fiscal Year Final Research Report Summary
Web geometry, geometry of surfaces with codimension 2 and their applications to singularity theory
| Project/Area Number |
16540090
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Kure National College of Technology |
|---|
Principal Investigator |
KUROKAWA Yasuhiro Kure National College of Technology, General Education, Assistant Professor (40353312)
|
|---|
| Project Period (FY) |
2004 – 2006
|
| Keywords | web / singular point / surface / asymptotic line / 4 dimension / inflection point / binary differential equation |
|---|
| Research Abstract |
1. Geometry of surfaces with codimension 2 in 4-space
In this research we have investigated singularities for the asymptotic lines of generic surfaces with codimension 2 around isolated inflection points in 4-spaces. The singularities corresponds to singularities of certain class of binary differential equations. In this case the simple singularities is of type Dl, D2, D3. Also appear more degenerated singularities, which is called type D23. We give the phase portrait of type D23.
2. Linearization of web structure
A configurations of functions with isolated singularities gives a web structure. It seems that a finite determined theory in singularity theory is useful to study linearization problem of webs.
|
