Bull. Korean Math. Soc. 1998; 35(4): 669-679
Printed December 1, 1998
Copyright © The Korean Mathematical Society.
Eun Sook Bang, Seoung Dal Jung, and Jin Suk Pak
Cheju National University, Cheju National University, Kyungpook National University
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
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