Bulletin of the
Korean Mathematical Society BKMS

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 $M$.

Keywords: Clifford algebra, Clifford $L^2$-cohomology group, $L^2$-harmonic spinors, Dirac operator, spinor bundle

MSC numbers: 53A50