共形变换下极小子流形不变的条件

CONDITION FOR THE INVARIANCE OF MINIMAL SUBMANIFOLD UNDER ONFORMAL TRANSFOMATION

本文运用外微分运算的方法和在欧氏空间中将共形变换分解成若干个运动与反演变换的乘积的结果,得到在共形变换下极小子流形仍为极小子流形的条件。并且,由此得到一个推论。

In this article,by make use of the exterier differential calculus and secparateof the conformal transformation into several products of movoment and inversiontransformation in Euclidean Space.We can get the conditions that the minimalsubmanifold keep to itself under the conformal transformation and from them weget a corollary.