{"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":"<p>In this paper, we study Lagrangian submanifolds of the pseudo-nearly Kähler <span></span><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.</p>","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\":\"<p>In this paper, we study Lagrangian submanifolds of the pseudo-nearly Kähler <span></span><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.</p>\",\"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。
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 . 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.
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