子流形的高斯映照(Ⅰ)

On the Gauss Map of Submanifolds (Ⅰ)

设Ｎ 是欧氏空间Ｅｎ ＋ １ 中的超曲面，Ｍ 是Ｎ 的子流形．本文研究 Ｍ 上的高斯映照，计算高斯映照的微分，由此建立起Ｍ 的Ｒｉｃｃｉ 形式与第二。

Let N be a hypersurface of the Euclidean space E n+1 , and M be an submanifold isometrically immersed in N . In this paper, the Gauss map of M is studied. By determining the differential of the Gauss map, the relationship among the Ricci curvature, the second and the third fundamental forms of M is establish.