A relation between the curvature ellipse and the curvature parabola
A relation between the curvature ellipse and the curvature parabola
复制标题
曲率椭圆和曲率抛物线之间的关系
DOI：
10.1515/advgeom-2019-0002
复制
发表时间：
2017
影响因子：
0.5
通讯作者：
P. B. Riul
中科院分区：
文献类型：
--
作者：
R. O. Sinha;P. B. Riul
在一个浸入曲面中的每一点上，在法平面上都有一个曲率椭圆，它将曲面的所有局部二阶几何编码。最近，在一个corank 1奇异曲面的奇点上，在法平面上定义了一个曲率抛物线，它将所有的局部二阶几何编码起来。当在切线方向上投影一个从λ 4到λ 3的规则曲面时，一般会出现corank 1奇点。除非投影方向是渐近的，否则投影具有交叉帽奇异性，在渐近方向上可能出现更多的退化奇异性。在本文中，我们涉及到的几何浸入表面在某一点上，在奇点的几何投影的表面到EZ3在EZ4。特别地，我们将曲面的曲率椭圆与其奇异投影的曲率抛物线联系起来。
At each point in an immersed surface in ℝ4 there is a curvature ellipse in the normal plane which codifies all the local second order geometry of the surface. Recently, at the singular point of a corank 1 singular surface in ℝ3, a curvature parabola in the normal plane which codifies all the local second order geometry has been defined. When projecting a regular surface in ℝ4 to ℝ3 in a tangent direction, corank 1 singularities appear generically. The projection has a cross-cap singularity unless the direction of projection is asymptotic, where more degenerate singularities can appear. In this paper we relate the geometry of an immersed surface in ℝ4 at a certain point to the geometry of the projection of the surface to ℝ3 at the singular point. In particular we relate the curvature ellipse of the surface to the curvature parabola of its singular projection.
DOI：
10.1142/9108
发表时间：
2015-12
期刊：
--
影响因子：
--
作者：
S. Izumiya;M. Fuster;M. Ruas;F. Tari
通讯作者：
S. Izumiya;M. Fuster;M. Ruas;F. Tari