{"title":"复杂两平面Grassmannians中等距Reeb流实超曲面的一些新特征","authors":"Dehe Li, Bo Li, Lifen Zhang","doi":"10.1155/2023/2347915","DOIUrl":null,"url":null,"abstract":"<jats:p>In this note, we establish an integral inequality for compact and orientable real hypersurfaces in complex two-plane Grassmannians <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\n <msub>\n <mrow>\n <mi>G</mi>\n </mrow>\n <mrow>\n <mn>2</mn>\n </mrow>\n </msub>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <msup>\n <mrow>\n <mi>ℂ</mi>\n </mrow>\n <mrow>\n <mi>m</mi>\n <mo>+</mo>\n <mn>2</mn>\n </mrow>\n </msup>\n </mrow>\n </mfenced>\n </math>\n </jats:inline-formula>, involving the shape operator <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\n <mi>A</mi>\n </math>\n </jats:inline-formula> and the Reeb vector field <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\n <mi>ξ</mi>\n </math>\n </jats:inline-formula>. Moreover, this integral inequality is optimal in the sense that the real hypersurfaces attaining the equality are completely determined. As direct consequences, some new characterizations of the real hypersurfaces in <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\n <msub>\n <mrow>\n <mi>G</mi>\n </mrow>\n <mrow>\n <mn>2</mn>\n </mrow>\n </msub>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <msup>\n <mrow>\n <mi>ℂ</mi>\n </mrow>\n <mrow>\n <mi>m</mi>\n <mo>+</mo>\n <mn>2</mn>\n </mrow>\n </msup>\n </mrow>\n </mfenced>\n </math>\n </jats:inline-formula> with isometric Reeb flow can be presented.</jats:p>","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some New Characterizations of Real Hypersurfaces with Isometric Reeb Flow in Complex Two-Plane Grassmannians\",\"authors\":\"Dehe Li, Bo Li, Lifen Zhang\",\"doi\":\"10.1155/2023/2347915\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<jats:p>In this note, we establish an integral inequality for compact and orientable real hypersurfaces in complex two-plane Grassmannians <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M1\\\">\\n <msub>\\n <mrow>\\n <mi>G</mi>\\n </mrow>\\n <mrow>\\n <mn>2</mn>\\n </mrow>\\n </msub>\\n <mfenced open=\\\"(\\\" close=\\\")\\\">\\n <mrow>\\n <msup>\\n <mrow>\\n <mi>ℂ</mi>\\n </mrow>\\n <mrow>\\n <mi>m</mi>\\n <mo>+</mo>\\n <mn>2</mn>\\n </mrow>\\n </msup>\\n </mrow>\\n </mfenced>\\n </math>\\n </jats:inline-formula>, involving the shape operator <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M2\\\">\\n <mi>A</mi>\\n </math>\\n </jats:inline-formula> and the Reeb vector field <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M3\\\">\\n <mi>ξ</mi>\\n </math>\\n </jats:inline-formula>. Moreover, this integral inequality is optimal in the sense that the real hypersurfaces attaining the equality are completely determined. As direct consequences, some new characterizations of the real hypersurfaces in <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M4\\\">\\n <msub>\\n <mrow>\\n <mi>G</mi>\\n </mrow>\\n <mrow>\\n <mn>2</mn>\\n </mrow>\\n </msub>\\n <mfenced open=\\\"(\\\" close=\\\")\\\">\\n <mrow>\\n <msup>\\n <mrow>\\n <mi>ℂ</mi>\\n </mrow>\\n <mrow>\\n <mi>m</mi>\\n <mo>+</mo>\\n <mn>2</mn>\\n </mrow>\\n </msup>\\n </mrow>\\n </mfenced>\\n </math>\\n </jats:inline-formula> with isometric Reeb flow can be presented.</jats:p>\",\"PeriodicalId\":49111,\"journal\":{\"name\":\"Advances in Mathematical Physics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-03-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1155/2023/2347915\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1155/2023/2347915","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
Some New Characterizations of Real Hypersurfaces with Isometric Reeb Flow in Complex Two-Plane Grassmannians
In this note, we establish an integral inequality for compact and orientable real hypersurfaces in complex two-plane Grassmannians , involving the shape operator and the Reeb vector field . Moreover, this integral inequality is optimal in the sense that the real hypersurfaces attaining the equality are completely determined. As direct consequences, some new characterizations of the real hypersurfaces in with isometric Reeb flow can be presented.
期刊介绍：
Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike.
As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.
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