{"title":"Para-Sasakian \\(\\phi -\\)symmetric spaces","authors":"Eugenia Loiudice","doi":"10.1007/s10455-024-09980-x","DOIUrl":null,"url":null,"abstract":"<div><p>We study the Boothby–Wang fibration of para-Sasakian manifolds and introduce the class of para-Sasakian <span>\\(\\phi \\)</span>-symmetric spaces, canonically fibering over para-Hermitian symmetric spaces. We remark that in contrast to the Hermitian setting the center of the isotropy group of a simple para-Hermitian symmetric space <i>G</i>/<i>H</i> can be either one- or two-dimensional, and prove that the associated metric is not necessarily the <i>G</i>-invariant extension of the Killing form of <i>G</i>. Using the Boothby–Wang fibration and the classification of semisimple para-Hermitian symmetric spaces, we explicitly construct semisimple para-Sasakian <span>\\(\\phi \\)</span>-symmetric spaces fibering over semisimple para-Hermitian symmetric spaces. We provide moreover an example of non-semisimple para-Sasakian <span>\\(\\phi \\)</span>-symmetric space.\n</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"67 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-024-09980-x.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Global Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10455-024-09980-x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We study the Boothby–Wang fibration of para-Sasakian manifolds and introduce the class of para-Sasakian \(\phi \)-symmetric spaces, canonically fibering over para-Hermitian symmetric spaces. We remark that in contrast to the Hermitian setting the center of the isotropy group of a simple para-Hermitian symmetric space G/H can be either one- or two-dimensional, and prove that the associated metric is not necessarily the G-invariant extension of the Killing form of G. Using the Boothby–Wang fibration and the classification of semisimple para-Hermitian symmetric spaces, we explicitly construct semisimple para-Sasakian \(\phi \)-symmetric spaces fibering over semisimple para-Hermitian symmetric spaces. We provide moreover an example of non-semisimple para-Sasakian \(\phi \)-symmetric space.
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.