CLIFFORD $L^2$-COHOMOLOGY ON THE COMPLETE KAHLER MANIFOLDS II

  • Bang, Eun-Sook (Department of Mathematics, Cheju National University) ;
  • Jung, Seoung-Dal (Department of Mathematics, Cheju National University) ;
  • Pak, Jin-Suk (Department of Mathematics, Kyungpook National University)
  • Published : 1998.11.01

Abstract

In this paper, we prove that on the complete Kahler manifold, if ${\rho}(x){\geq}-\frac{1}{2}{\lambda}_0$ and either ${\rho}(x_0)>-\frac{1}{2}{lambda}_0$ at some point $x_0$ or Vol(M)=${\infty}$, then the Clifford $L^2$ cohomology group $L^2{\mathcal H}^{\ast}(M,S)$ is trivial, where $\rho(x)$ is the least eigenvalue of ${\mathcal R}_x + \bar{{\mathcal R}}(x)\;and\;{\lambda}_0$ is the infimum of the spectrum of the Laplacian acting on $L^2$-functions on M.