伪近似 Kähler SL(2,R)×SL(2,R)$\mathrm{SL}(2,\mathbb {R})\times \mathrm{SL}(2,\mathbb {R})$ 的完全测地拉格朗日子网格

Pub Date : 2024-03-03 DOI:10.1002/mana.202300351

Mateo Anarella, J. Van der Veken

{"title":"伪近似 Kähler SL(2,R)×SL(2,R)$\\mathrm{SL}(2,\\mathbb {R})\\times \\mathrm{SL}(2,\\mathbb {R})$ 的完全测地拉格朗日子网格","authors":"Mateo Anarella, J. Van der Veken","doi":"10.1002/mana.202300351","DOIUrl":null,"url":null,"abstract":"In this paper, we study Lagrangian submanifolds of the pseudo-nearly Kähler <math>\n <semantics>\n <mrow>\n <mi>SL</mi>\n <mo>(</mo>\n <mn>2</mn>\n <mo>,</mo>\n <mi>R</mi>\n <mo>)</mo>\n <mo>×</mo>\n <mi>SL</mi>\n <mo>(</mo>\n <mn>2</mn>\n <mo>,</mo>\n <mi>R</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$\\mathrm{SL}(2,\\mathbb {R})\\times \\mathrm{SL}(2,\\mathbb {R})$</annotation>\n </semantics></math>. First, we show that they split into four different classes depending on their behavior with respect to a certain almost product structure on the ambient space. Then, we give a complete classification of totally geodesic Lagrangian submanifolds of this space.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Totally geodesic Lagrangian submanifolds of the pseudo-nearly Kähler \\n \\n \\n SL\\n (\\n 2\\n ,\\n R\\n )\\n ×\\n SL\\n (\\n 2\\n ,\\n R\\n )\\n \\n $\\\\mathrm{SL}(2,\\\\mathbb {R})\\\\times \\\\mathrm{SL}(2,\\\\mathbb {R})$\",\"authors\":\"Mateo Anarella, J. Van der Veken\",\"doi\":\"10.1002/mana.202300351\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study Lagrangian submanifolds of the pseudo-nearly Kähler <math>\\n <semantics>\\n <mrow>\\n <mi>SL</mi>\\n <mo>(</mo>\\n <mn>2</mn>\\n <mo>,</mo>\\n <mi>R</mi>\\n <mo>)</mo>\\n <mo>×</mo>\\n <mi>SL</mi>\\n <mo>(</mo>\\n <mn>2</mn>\\n <mo>,</mo>\\n <mi>R</mi>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$\\\\mathrm{SL}(2,\\\\mathbb {R})\\\\times \\\\mathrm{SL}(2,\\\\mathbb {R})$</annotation>\\n </semantics></math>. First, we show that they split into four different classes depending on their behavior with respect to a certain almost product structure on the ambient space. Then, we give a complete classification of totally geodesic Lagrangian submanifolds of this space.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-03-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mana.202300351\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mana.202300351","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们研究了伪近似凯勒的拉格朗日子漫空间（Lagrangian submanifolds of the pseudo-nearly Kähler .首先，我们证明了它们分为四个不同的类别，这取决于它们相对于环境空间上的某种近积结构的行为。然后，我们给出了该空间的完全测地拉格朗日子实体的完整分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

Totally geodesic Lagrangian submanifolds of the pseudo-nearly Kähler SL ( 2 , R ) × SL ( 2 , R ) $\mathrm{SL}(2,\mathbb {R})\times \mathrm{SL}(2,\mathbb {R})$

In this paper, we study Lagrangian submanifolds of the pseudo-nearly Kähler $SL (2, R) \times SL (2, R)$ . First, we show that they split into four different classes depending on their behavior with respect to a certain almost product structure on the ambient space. Then, we give a complete classification of totally geodesic Lagrangian submanifolds of this space.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助