HUSCAP logo Hokkaido Univ. logo

Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
北海道大学数学講究録 = Hokkaido University technical report series in mathematics >

Doctoral thesis Affine geometry of space curves and homogeneous surfaces

Files in This Item:
tech154.pdf674.79 kBPDFView/Open
Please use this identifier to cite or link to this item:https://doi.org/10.14943/81516

Title: Doctoral thesis Affine geometry of space curves and homogeneous surfaces
Authors: Hu, Na Browse this author
Issue Date: 16-Aug-2012
Journal Title: Hokkaido University technical report series in mathematics
Journal Title(alt): 北海道大学数学講究録
Volume: 154
Start Page: i, 1
End Page: iii, 65
Abstract: We investigate the centroaffine space curves with constant centroaffine curvatures in R3. We classify them and give their explicit expressions. Moreover, we find out each centroaffine space curve with constant centroaffine curvatures can be written as the orbit of a certain one-parameter subgroup of GL(3,R). Thus we can treat them as nondegenerate centroaffine homogeneous curves. Furthermore, for each centroaffine homogeneous curve, we check if there is a nondegenerate centroaffine homogeneous surface such that the corresponding group contains exactly, as a subgroup, the one-parameter subgroup with respect to the homogeneous curve. We obtain the similar results for equiaffine space curves with constant equiaffine curvatures. At the end, we bring up a related topic of the centroaffine space curve theory, degenerate center maps. We investigate centroaffine ruled surfaces and determine such surfaces whose center map is degenerate. As a corollary, given a nondegenerate centroaffine space curve, we can construct a centroaffine ruled surface whose center map is precisely this curve.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/68078
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 北海道大学数学講究録 = Hokkaido University technical report series in mathematics

Submitter: 数学紀要登録作業用

Export metadata:

OAI-PMH ( junii2 , jpcoar_1.0 )

MathJax is now OFF:


 

 - Hokkaido University