On Compact Hypersurface of an even-dimensional Sphere

Abstract

偶數次元 球面의 完閉 可符號인 超曲面에서 다음 命題가 同値이다.

(1) α²+β²+λ²=1.

(2) U는 平行 vector 場이다.

(3) h (X,Y)=??g(X,Y).

Let M be a compact orientable hypersurface of an even dimensional sphere. Then the following statements are equivalent;

(1) α²+β²+λ²=1,

(2) U is a parallel vector field,

(3) h (X,Y)=??g(X,Y).

Let M be a compact orientable hypersurface of an even dimensional sphere. Then the following statements are equivalent;

(1) α²+β²+λ²=1,

(2) U is a parallel vector field,

(3) h (X,Y)=??g(X,Y).