Some New Characterizations of Real Hypersurfaces with Isometric Reeb Flow in Complex Two-Plane Grassmannians

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Advances in Mathematical Physics Pub Date : 2023-03-10 DOI:10.1155/2023/2347915

Dehe Li, Bo Li, Lifen Zhang

{"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":"In this note, we establish an integral inequality for compact and orientable real hypersurfaces in complex two-plane Grassmannians \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 , involving the shape operator \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\n <mi>A</mi>\n </math>\n and the Reeb vector field \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\n <mi>ξ</mi>\n </math>\n . 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 \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 with isometric Reeb flow can be presented.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"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}

引用次数: 0

Abstract

In this note, we establish an integral inequality for compact and orientable real hypersurfaces in complex two-plane Grassmannians

G_{2} (ℂ^{m + 2})

, involving the shape operator

A

and the Reeb vector field

ξ

. 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

G_{2} (ℂ^{m + 2})

with isometric Reeb flow can be presented.

查看原文本刊更多论文

复杂两平面Grassmannians中等距Reeb流实超曲面的一些新特征

在该注释中，我们在复二平面Grassmannians G2中建立了紧致可定向实超曲面的一个积分不等式ℂ m+2，涉及形状算子A和Reeb向量场ξ。此外，这个积分不等式在达到等式的实超曲面是完全确定的意义上是最优的。作为直接后果，G2中实超曲面的一些新性质ℂ m+2具有等距Reeb流。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Advances in Mathematical Physics 数学-应用数学

CiteScore

2.40

自引率

8.30%

发文量

151

审稿时长

>12 weeks

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.