极小子流形上Laplace算子的谱

On the Spectrum of the Laplacian Operators on Minimal Submanifolds

本文讨论了Ｓｎ＋ｐ（１）（或ＣＰｎ＋１）中极小子流形上Ｌａｐｌａｃｅ算子的谱，证明了Ｓｎ＋ｐ（１）中全测地极小子流形（或ＣＰｎ＋１中Ｋａｃｈｌｅｒ超曲面）是由作用在ｑ形式上的Ｌａｐｌａｃｅ算子的谱唯一确定．

In the present paper we discuss the spectrum of Laplacian on minimal submanifolds of S n+p (1) or CP n+1 , and prove that the totally geodesic minimal submanifold of S n+p (1) and the Kaehler hypersurface of CP n+1 have been uniquely characterized by spectrum of q forms of the Laplacian on them.