A VANISHING THEOREM ON L2 HARMONIC FORMS

摘要

This paper is concernod with the L2 harmonic forms of a complete noncompact Riemannian manifold, i.e. If M has a pole Q, let 0 ＜ p ＜ n/1+ 2 or 2n/1+ 2 ＜ p ＜ n, and assume the radial section curvatures satisfy -c(1-c)/r2 ≤ Kr ≤ c(1-c)/r2 on M - {Q}, where 1＞c＞ (1+ 2)p-1-1, then Hp = {0}. If M has a soul, then similar result is obtained.