Immersions of Sasaki–Ricci solitons into homogeneous Sasakian manifolds

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2023-12-14 DOI:10.1007/s10455-023-09939-4

R. Mossa, G. Placini

引用次数: 0

Abstract

We discuss local Sasakian immersion of Sasaki–Ricci solitons (SRS) into fiber products of homogeneous Sasakian manifolds. In particular, we prove that SRS locally induced by a large class of fiber products of homogeneous Sasakian manifolds are, in fact, \(\eta \)-Einstein. The results are stronger for immersions into Sasakian space forms. Moreover, we show an example of a Kähler–Ricci soliton on \(\mathbb C^n\) which admits no local holomorphic isometry into products of homogeneous bounded domains with flat Kähler manifolds and generalized flag manifolds.

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佐佐木-里奇孤子在均质佐佐木流形中的沉浸

讨论了Sasaki-Ricci孤子(SRS)在均匀sasaki流形纤维产物中的局部sasaki浸入。特别地，我们证明了由一大类齐次sasaki流形的纤维积局部诱导的SRS实际上是\(\eta \) -爱因斯坦。沉浸在sasaki空间形式中的结果更强。此外，我们还给出了一个在\(\mathbb C^n\)上的Kähler-Ricci孤子的例子，该孤子不允许局部全纯等边化为平坦Kähler流形和广义标志流形的齐次有界域积。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.