R^4中曲面不变量的切指标线和法曲率椭圆的几何解释
Geometric interpretation of the invariants of a surface in R^4 via the tangent indicatrix and the normal curvature ellipse
摘要：
在四维欧几里得空间中的曲面的任何一点上，我们考虑由两个图形组成的几何构形：切指标线，它是切面中的圆锥曲线，和法曲率椭圆。我们表明，在四维欧几里得空间，由其不变量的条件确定的基本几何类的表面，可以解释的两个几何图形的属性。我们给出了一些非平凡的例子，从考虑类的表面。
英文摘要：
At any point of a surface in the four-dimensional Euclidean space we consider the geometric configuration consisting of two figures: the tangent indicatrix, which is a conic in the tangent plane, and the normal curvature ellipse. We show that the basic geometric classes of surfaces in the four-dimensional Euclidean space, determined by conditions on their invariants, can be interpreted in terms of the properties of the two geometric figures. We give some non-trivial examples of surfaces from the classes in consideration.
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