Adapted metrics on locally conformally product manifolds

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-03-07 DOI:10.1090/proc/16706

Andrei Moroianu, Mihaela Pilca

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引用次数: 0

Abstract

We show that the Gauduchon metric g 0 g_0 of a compact locally conformally product manifold ( M , c , D ) (M,c,D) of dimension greater than 2 2 is adapted, in the sense that the Lee form of D D with respect to g 0 g_0 vanishes on the D D -flat distribution of M M . We also characterize adapted metrics as critical points of a natural functional defined on the conformal class.

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局部保角积流形上的适应度量

我们证明，维度大于 2 2 的紧凑局部保角积流形 ( M , c , D ) (M,c,D) 的高都松度量 g 0 g_0 是自适应的，即 D D 关于 g 0 g_0 的李形式在 M M 的 D D 平面分布上消失。我们还将适配度量描述为定义在共形类上的自然函数的临界点。

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.