关于积流形的P－形式上的Laplace算子谱

On the Laplacian Spectrum on the p-forms on on the Product Riemannian Manifolds

本文讨论了积流形的Ｐ－形式上Ｌａｐｌａｃｅ算子谱的唯一性问题，在紧Ｋａｃｈｌｅｒ流形乘积和紧Ｓａｓａｋｉ流形乘积的两类积流形中，ＣＰ￣ｎ×ＣＰ￣ｎ和Ｓ￣（２ｎ＋１）（１）×Ｓ￣（２ｎ＋１）（１）是Ｐ－形式上Ｌａｐｌａｃｃｅ算子谱特征。

In this paper,it is proved that CP￣n ×CP￣n and S￣(2n+1)×S￣(2n+1)(1)are uniquelycharacterized among the classes of the Riemannian products of compact Kachler mani-folds and the Riemannian products of compact Sasakian manifolds,respectively,by theLaplacian spectrum on p- forms for some p。