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CLIFFORD $L^2$-COHOMOLOGY ON THE COMPLETE $K\"{A}$HLER MANIFOLDS

  • Pak, Jin-Suk;Jung, Seoung-Dal
    • Journal of the Korean Mathematical Society
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    • v.34 no.1
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    • pp.167-179
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    • 1997
  • In the study of a manifold M, the exterior algebra $\Lambda^* M$ plays an important role. In fact, the de Rham cohomology theory gives many informations of a manifold. Another important object in the study of a manifold is its Clifford algebra (Cl(M), generated by the tangent space.

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

  • Bang, Eun-Sook;Jung, Seoung-Dal;Pak, Jin-Suk
    • Bulletin of the Korean Mathematical Society
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    • v.35 no.4
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    • pp.669-681
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    • 1998
  • 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.

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