Inhomogeneous deformations of Einstein solvmanifolds

IF 1.2 2区数学 Q1 MATHEMATICS Journal of the London Mathematical Society-Second Series Pub Date : 2024-04-30 DOI:10.1112/jlms.12904

Adam Thompson

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引用次数: 0

Abstract

For each non-flat, unimodular Ricci soliton solvmanifold $(S_{0}, g_{0})$ , we construct a one-parameter family of complete, expanding, gradient Ricci solitons that admit a cohomogeneity one isometric action by $S_{0}$ . The orbits of this action are hypersurfaces homothetic to $(S_{0}, g_{0})$ . These metrics are asymptotic at one end to an Einstein solvmanifold. In the one-parameter family, exactly one metric is Einstein, and exactly one has orbits that are isometric to $(S_{0}, g_{0})$ .

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爱因斯坦求解漫流的非均质变形

对于每一个非平坦、单模态的利玛窦孤素解旋体( S 0 , g 0 ) $ (\mathsf {S}_0,g_0)$ ，我们构建了一个完整的、扩展的、梯度的利玛窦孤素的单参数族，该族通过 S 0 $\mathsf {S}_0$ 接受同构一等轴作用。该作用的轨道是与 ( S 0 , g 0 ) $(\mathsf {S}_0,g_0)$ 同调的超曲面。这些度量在一端渐近于爱因斯坦溶域。在单参数族中，正好有一个度量是爱因斯坦度量，正好有一个度量的轨道与 ( S 0 , g 0 ) $(\mathsf {S}_0,g_0)$ 等距。

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.

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