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Conformal Operators on Weighted Forms; Their Decomposition and Null Space on Einstein Manifolds

机译:加权表格上的保形运算符;它们在爱因斯坦流形上的分解和零空间

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摘要

There is a class of Laplacian like conformally invariant differential operators on differential forms L_k~? which may be considered as the generalisation to differential forms of the conformally invariant powers of the Laplacian known as the Paneitz and GJMS operators. On conformally Einstein manifolds we give explicit formulae for these as factored polynomials in second-order differential operators. In the case that the manifold is not Ricci flat we use this to provide a direct sum decomposition of the null space of the L_k~? in terms of the null spaces of mutually commuting second-order factors.
机译:在微分形式L_k〜?上有一类Laplacian像保形不变的微分算子。可以认为是对拉普拉斯算子不变的幂的微分形式的泛化,称为Paneitz和GJMS运算符。在保形爱因斯坦流形上,我们给出了作为二阶微分算子的阶乘多项式的显式公式。在流形不是Ricci平面的情况下,我们使用它来提供L_k〜?的零空间的直接和分解。就互通二阶因子的零空间而言。

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