Inflection points and topology of surfaces in 4-space
Inflection points and topology of surfaces in 4-space
复制标题
4 空间中曲面的拐点和拓扑
DOI：
10.1090/s0002-9947-00-02404-1
复制
发表时间：
2000
影响因子：
1.3
通讯作者：
M. Ruas
中科院分区：
文献类型：
--
作者：
Ronaldo Garcia;D. Mochida;M. Fuster;M. Ruas
我们考虑 4 空间中通用曲面上的渐近线场，并表明它们是在局部凸曲面上全局定义的，并且它们的奇点是曲面的拐点。根据广义庞加莱-霍普夫公式，我们得到了泛型曲面中的拐点数量与其欧拉数之间的一些关系。特别是，任何 2-球体（一般作为局部凸面嵌入到 4-空间中）都具有至少 4 个拐点。
We consider asymptotic line fields on generic surfaces in 4-space and show that they are globally defined on locally convex surfaces, and their singularities are the inflection points of the surface. As a consequence of the generalized Poincare-Hopf formula, we obtain some relations between the number of inflection points in a generic surface and its Euler number. In particular, it follows that any 2-sphere, generically embedded as a locally convex surface in 4-space, has at least 4 inflection points.