Lorentz-Minkowski空间中满足L_r x =U x +b的归一化零超曲面

IF 0.7 Q2 MATHEMATICS
Hans FOTSING TETSING, C. Atindogbe, Ferdinand Nkageu
{"title":"Lorentz-Minkowski空间中满足L_r x =U x +b的归一化零超曲面","authors":"Hans FOTSING TETSING, C. Atindogbe, Ferdinand Nkageu","doi":"10.5556/j.tkjm.54.2023.4851","DOIUrl":null,"url":null,"abstract":"In the present paper, we classify all normalized null hypersurfaces $x: (M,g,N)\\to\\R^{n+2}_1$ endowed with UCC-normalization with vanishing $1-$form $\\tau$, satisfying $L_r x =U x +b$ for some (field of) screen constant matrix $U\\in \\R^{(n+2)\\times(n+2)}$ and vector$b\\in\\R^{n+2}_{1}$, where $L_r$ is the linearized operator of the$(r+1)th-$mean curvature of the normalized null hypersurface for$r=0,...,n$. For $r=0$, $L_0=\\Delta^\\eta$ is nothing but the (pseudo-)Laplacian operator on $(M, g, N)$. We prove that the lightcone $\\Lambda_0^{n+1}$, lightcone cylinders $\\Lambda_0^{m+1}\\times\\R^{n-m}$, $1\\leq m\\leq n-1$ and $(r+1)-$maximal Monge null hypersurfaces are the only UCC-normalized Monge null hypersurface with vanishing normalization $1-$form $\\tau$ satisfying the above equation. In case $U$ is the (field of) scalar matrix $ \\lambda I$, $\\lambda\\in\\R$ and hence is constant on the whole $M$, we show that the only normalized Monge null hypersurfaces $x: (M,g,N)\\to\\R^{n+2}_1$ satisfying $\\Delta^\\eta x =\\lambda x +b$, are open pieces of hyperplanes.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"40 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2022-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Normalized null hypersurfaces in the Lorentz-Minkowski space satisfying $L_r x =U x +b$\",\"authors\":\"Hans FOTSING TETSING, C. Atindogbe, Ferdinand Nkageu\",\"doi\":\"10.5556/j.tkjm.54.2023.4851\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the present paper, we classify all normalized null hypersurfaces $x: (M,g,N)\\\\to\\\\R^{n+2}_1$ endowed with UCC-normalization with vanishing $1-$form $\\\\tau$, satisfying $L_r x =U x +b$ for some (field of) screen constant matrix $U\\\\in \\\\R^{(n+2)\\\\times(n+2)}$ and vector$b\\\\in\\\\R^{n+2}_{1}$, where $L_r$ is the linearized operator of the$(r+1)th-$mean curvature of the normalized null hypersurface for$r=0,...,n$. For $r=0$, $L_0=\\\\Delta^\\\\eta$ is nothing but the (pseudo-)Laplacian operator on $(M, g, N)$. We prove that the lightcone $\\\\Lambda_0^{n+1}$, lightcone cylinders $\\\\Lambda_0^{m+1}\\\\times\\\\R^{n-m}$, $1\\\\leq m\\\\leq n-1$ and $(r+1)-$maximal Monge null hypersurfaces are the only UCC-normalized Monge null hypersurface with vanishing normalization $1-$form $\\\\tau$ satisfying the above equation. In case $U$ is the (field of) scalar matrix $ \\\\lambda I$, $\\\\lambda\\\\in\\\\R$ and hence is constant on the whole $M$, we show that the only normalized Monge null hypersurfaces $x: (M,g,N)\\\\to\\\\R^{n+2}_1$ satisfying $\\\\Delta^\\\\eta x =\\\\lambda x +b$, are open pieces of hyperplanes.\",\"PeriodicalId\":45776,\"journal\":{\"name\":\"Tamkang Journal of Mathematics\",\"volume\":\"40 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-08-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tamkang Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5556/j.tkjm.54.2023.4851\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tamkang Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5556/j.tkjm.54.2023.4851","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1

摘要

本文对具有ucc归一化的所有归一化空超曲面$x: (M,g,N)\to\R^{n+2}_1$进行了分类,其中$L_r$是$r=0,...,n$归一化空超曲面$(r+1)th-$的平均曲率的线性化算子,并将$1-$从$\tau$中消失,满足$L_r x =U x +b$的屏幕常数矩阵$U\in \R^{(n+2)\times(n+2)}$和向量$b\in\R^{n+2}_{1}$。对于$r=0$, $L_0=\Delta^\eta$只是$(M, g, N)$上的(伪)拉普拉斯运算符。我们证明了光锥$\Lambda_0^{n+1}$、光锥柱面$\Lambda_0^{m+1}\times\R^{n-m}$、$1\leq m\leq n-1$和$(r+1)-$是满足上述方程的唯一具有消失归一化形式$1-$$\tau$的ucc归一化的最大Monge零超曲面。如果$U$是标量矩阵$ \lambda I$, $\lambda\in\R$的(域),因此在整个$M$上是常数,我们证明了满足$\Delta^\eta x =\lambda x +b$的唯一归一化的Monge零超曲面$x: (M,g,N)\to\R^{n+2}_1$是超平面的开放块。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Normalized null hypersurfaces in the Lorentz-Minkowski space satisfying $L_r x =U x +b$
In the present paper, we classify all normalized null hypersurfaces $x: (M,g,N)\to\R^{n+2}_1$ endowed with UCC-normalization with vanishing $1-$form $\tau$, satisfying $L_r x =U x +b$ for some (field of) screen constant matrix $U\in \R^{(n+2)\times(n+2)}$ and vector$b\in\R^{n+2}_{1}$, where $L_r$ is the linearized operator of the$(r+1)th-$mean curvature of the normalized null hypersurface for$r=0,...,n$. For $r=0$, $L_0=\Delta^\eta$ is nothing but the (pseudo-)Laplacian operator on $(M, g, N)$. We prove that the lightcone $\Lambda_0^{n+1}$, lightcone cylinders $\Lambda_0^{m+1}\times\R^{n-m}$, $1\leq m\leq n-1$ and $(r+1)-$maximal Monge null hypersurfaces are the only UCC-normalized Monge null hypersurface with vanishing normalization $1-$form $\tau$ satisfying the above equation. In case $U$ is the (field of) scalar matrix $ \lambda I$, $\lambda\in\R$ and hence is constant on the whole $M$, we show that the only normalized Monge null hypersurfaces $x: (M,g,N)\to\R^{n+2}_1$ satisfying $\Delta^\eta x =\lambda x +b$, are open pieces of hyperplanes.
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
来源期刊
CiteScore
1.50
自引率
0.00%
发文量
11
期刊介绍: To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers in pure and applied mathematics. In 1985 it has become a quarterly journal. The four issues are out for distribution at the end of March, June, September and December. The articles published in Tamkang Journal of Mathematics cover diverse mathematical disciplines. Submission of papers comes from all over the world. All articles are subjected to peer review from an international pool of referees.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信