Clifford $L^2$ cohomology on the complete Kahler manifolds II

Bull. Korean Math. Soc. 1998 Vol. 35, No. 4, 669-679

Eun Sook Bang, Seoung Dal Jung, and Jin Suk Pak Cheju National University, Cheju National University, Kyungpook National University

Abstract : In this paper, we prove that on the complete K\"ahler manifold, if $\rho(x)\geq -\frac12\lambda_0$ and either $\rho(x_0)>-\frac12\lambda_0$ at some point $x_0$ or $Vol(M)=\infty$, then the Clifford $L^2$-cohomology group $L^2\Cal H^*(M,S)$ is trivial, where $\rho(x)$ is the least eigenvalue of $\Cal R_x +\bar\Cal R(x)$ and $\lambda_0$ is the infimum of the spectrum of the Laplacian acting on $L^2$- functions on $M$.