形式

Practical Bootstrap Pub Date : 1900-01-01 DOI:10.4337/9781788970228.00023

Panos Matsinopoulos

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引用次数: 0

摘要

。我们考虑是否有可能改进Novikov不等式对于封闭1-形式，或任何其他类似性质的不等式，如果我们另外假设，给定的1-形式对某些黎曼度规是调和的。我们证明，在适当的假设下，这是不可能的。我们使用E.Calabi [C]的一个定理，以一种基本的方式刻画了关于某个度规的调和1型。我们还研究了一些有趣的例子来说明我们的结果。

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Forms

. We consider the problem of whether it is possible to improve the Novikov inequalities for closed 1-forms, or any other inequalities of a similar nature, if we assume, additionally, that the given 1-form is harmonic with respect to some Riemannian metric. We show that, under suitable assumptions, it is impossible. We use a theorem of E.Calabi [C], characterizing 1-forms which are harmonic with respect to some metric, in an essential way. We also study some interesting examples illustrating our results.

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Practical Bootstrap

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