FLAT APPROXIMATIONS OF SURFACES ALONG CURVES

被引：22

作者：

Izumiya, Shyuichi ^{[1
]}

Otani, Saki ^{[2
]}

机构：

[1] Hokkaido Univ, Dept Math, Sapporo, Hokkaido 0600810, Japan

[2] Kyoritsu Shuppan Co Ltd, Bunkyo Ku, Tokyo 1128700, Japan

来源：

DEMONSTRATIO MATHEMATICA | 2015年 / 48卷 / 02期

关键词：

flat approximations; curves on surfaces; contour generators; developable surfaces;

D O I：

10.1515/dema-2015-0018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a developable surface tangent to a surface along a curve on the surface. We call it an osculating developable surface along the curve on the surface. We investigate the uniqueness and the singularities of such developable surfaces. We discover two new invariants of curves on a surface which characterize these singularities. As a by-product, we show that a curve is a contour generator with respect to an orthogonal projection or a central projection if and only if one of these invariants constantly equal to zero.

引用

页码：217 / 241

页数：25

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