作者： Li,Tongzhu¹;Ma,Xiang²;Wang,Changping³⁴;Wang,Peng³⁴; （¹Department of Mathematics, Beijing Institute of Technology, Beijing, China;²LMAM, School of Mathematical Sciences, Peking University, Beijing, China;³School of Mathematics and Statistics, FJKLAMA, Fujian Normal University, Fuzhou, China;⁴Key Laboratory of Analytical Mathematics and Applications, Ministry of Education, China）

出处： Advances in Mathematics 2024 Vol.448

摘要： Let M(Sn+1) denote the Möbius transformation group of the (n+1)-dimensional sphere Sn+1. A hypersurface x:Mn→Sn+1 is called a Möbius homogeneous hyper ...

作者： Li, Tongzhu¹;Lin, Ruiyang^1,2 （¹Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China.;²Beijing Key Lab MCAACI, Beijing 100081, Peoples R China.）

出处： AIMS MATHEMATICS 2024 Vol.9 No.8 P23027-23046

关键词： SUBMANIFOLDS; SPACE

摘要： In this paper, we investigate the Mobius geometry of curves in R4. 4 . First, using moving frame methods we construct a complete sy ...

作者： Yayun Chen;Tongzhu Li （¹Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China）

出处： Mathematics 2023 Vol.11 No.1435 P1435

关键词： generic conformally flat hypersurface;Möbius metric;Möbius form;Möbius curvature

摘要： A conformally flat hypersurface f:M3→R4 in the four-dimensional Euclidean space R4 is said to be generic if the hypersurface has three distinct princi ...

作者： Lin, Limiao¹;Li, Tongzhu² （¹Fujian Normal Univ, Sch Math & Stat, FJKLMAA, Fuzhou 350117, Peoples R China.;²Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China.）

出处： HOUSTON JOURNAL OF MATHEMATICS 2023 Vol.49 No.2 P305-323

关键词： MOBIUS ISOPARAMETRIC HYPERSURFACES; WILLMORE SURFACES; CLASSIFICATION; CURVATURE; SUBMANIFOLDS

摘要： Let x : Mn Sn+1 be an oriented immersed hypersurface in (n + 1)-dimensional sphere Sn+1 with a global unit normal vector field xi, then the conformal ...

作者： Chen, Yayun¹; Li, Tongzhu¹ （¹Department of Mathematics, Beijing Institute of Technology, Beijing; 100081, China）

出处： arXiv 2023

作者： Li, Tongzhu;Ma, Xiang;Wang, Changping;Wang, Peng （¹Department of Mathematics, Beijing Institute of Technology, Beijing, China;²LMAM, School of Mathematical Sciences, Peking University, Beijing, China;³College of Mathematics and Computer Science, Fujian Normal University, Fuzhou, China）

出处： arXiv 2022

摘要： Let M(Sn+1) denote the Möbius transformation group of the (n+1)-dimensional sphere Sn+1. A hypersurface x: Mn → Sn+1 is called a Möbius homogeneous hy ...

作者： 姬秀，李同柱 （北京理工大学数学与统计学院；北京理工大学数学与统计学院）

出处： 数学学报 2021 第64卷 第1期 P47-58

关键词： 共形度量；共形第二基本形式；共形拟Blaschke张量

摘要： 设f:M^m→R^m+1₁是无脐点类空超曲面,则在M^m上可以定义四个基本的共形不变量:共形度量g,共形1-形式C,共形第二基本形式B,共形Blaschke张量A.如果存在光滑函数λ和常数μ,使得A+μB=λg,则称M ...

作者： Xie, Zhenxiao¹;Li, Tongzhu²;Ma, Xiang³;Wang, Changping⁴; （¹Department of Mathematics, China University of Mining and Technology (Beijing), Beijing, 100083, China;²Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, China;³School of Mathematical Sciences, Peking University, Beijing, 100871, China;⁴School of Mathematics and Computer Science, FJKLMAA, Fujian Normal University, Fuzhou, 350108, China）

出处： Advances in Mathematics 2021 Vol.381 P107620

摘要： In real space forms, any submanifold must satisfy the so-called DDVV inequality which relates the scalar curvature, the mean curvature, and the scalar ...

作者： 陈芝红 （导师：李同柱）

学位名称： 硕士

出处： 北京理工大学 2017

作者： 韩希武 （导师：李同柱）

学位名称： 硕士

出处： 北京理工大学数学与统计学院 2016

关键词： 四元数；水印；线性正则变换；鲁棒性

摘要： 基于把水印分散于变换域上的水印算法的性能强烈依赖于核函数. 线性正则变换是傅里叶变换、分数阶傅里叶变换、Fresnel变换和缩放变换的一种推广. 线性正则变换是信号处理领域当中的一种重要工具. 二维线性正则变换是线性正则变换的进一步推广. 在本文中, 我们将二维线性正则变换推广到四元数域上, 将它命 ...