仿射空间R^（n＋1）中的非退化二次函数的水平曲面

LEVEL SURFACES FOR NON-DEGENERATE QUADRATIC FUNCTIONS IN THE AFFINE SPACE R￣(n+1)

本文利用Ｈｅｓｓｉａｎ度量和横截向量场，给出了非退化二次函数的水平曲面的一个充要条件．

In this paper,we give a sufficient and necessary condition for the level surfaces with respect to non-degenerate quadratic functions by the usage of the Hessian metric and of a transversal vector field.