We give a classification for connected complete locally irreducibleRiemannian manifolds with nonpositive curvature operator, which admit a nonzeroclosed or co-closed conformal Killing $L^{2}-$form. Moreover, we provevanishing theorems for closed and co-closed conformal Killing $L^{2}-$forms onsome complete Riemannian manifolds.
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机译:我们给出了一个带有非正曲率算子的连通完整局部不可约黎曼流形的分类,该流形承认一个非零闭合或共闭合的保形Kill $ L ^ {2}-$形式。此外,我们证明了一些完备的黎曼流形上的封闭和共封闭的共形Killing $ L ^ {2}-$形式的定理。
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