紧致连通曲面的法线特征

CHARACTERISTIC OF NORMAL LINE OF COMPACT CONNECTED SURFACES

利用Morse理论 ,给出紧致连通曲面的法线的一个很有趣的特征 :若S R3是亏格为 g的紧致连通曲面。则几乎对所有的p∈R3 ,S上至少有 2 +2g个点的法线经过 p。

Let SR 3 be a compact connected surface of genus g.Then for almost all p∈R 3,there are at least 2+2g line,which pass p and are normal to S.