{"title":"Pseudo-Riemannian and Hessian geometry related to Monge-Ampère structures","authors":"Radek Such'anek, Stanislav Hronek","doi":"10.5817/AM2022-5-329","DOIUrl":null,"url":null,"abstract":"We study properties of pseudo-Riemannian metrics corresponding to Monge-Amp\\`ere structures on four-dimensional $T^*M$. We describe a family of Ricci flat solutions, which are parametrized by six coefficients satisfying the Pl\\\"ucker embedding equation. We also focus on pullbacks of the pseudo-metrics on two-dimensional $M$ and describe the corresponding Hessian structures.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"131 5 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archivum Mathematicum","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5817/AM2022-5-329","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
We study properties of pseudo-Riemannian metrics corresponding to Monge-Amp\`ere structures on four-dimensional $T^*M$. We describe a family of Ricci flat solutions, which are parametrized by six coefficients satisfying the Pl\"ucker embedding equation. We also focus on pullbacks of the pseudo-metrics on two-dimensional $M$ and describe the corresponding Hessian structures.
期刊介绍：
Archivum Mathematicum is a mathematical journal which publishes exclusively scientific mathematical papers. The journal, founded in 1965, is published by the Department of Mathematics and Statistics of the Faculty of Science of Masaryk University. A review of each published paper appears in Mathematical Reviews and also in Zentralblatt für Mathematik. The journal is indexed by Scopus.
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