关于Veronese生成子流形的一个猜想

数学季刊 ›› 2004, Vol. 19 ›› Issue (1): 63-66.

关于Veronese生成子流形的一个猜想

College of Mathematics and Information Science, Henan University, Kaifeng 475001, China

收稿日期:2002-05-25 出版日期:2004-03-30 发布日期:2024-03-26
作者简介:SONG Hong-zao(1944-),male,native of Jiangyan,Jiangsu,a professor of Henan University, M.S.D.,engages in differential geometry.
基金资助:
Supported by the Education Commission of Henan Province(20021100002)； Supported by the NSF of Henan University(200110475028)；

A Conjecture on Veronese Generating Submanifolds

College of Mathematics and Information Science, Henan University, Kaifeng 475001, China

Received:2002-05-25 Online:2004-03-30 Published:2024-03-26
About author:SONG Hong-zao(1944-),male,native of Jiangyan,Jiangsu,a professor of Henan University, M.S.D.,engages in differential geometry.
Supported by:
Supported by the Education Commission of Henan Province(20021100002)； Supported by the NSF of Henan University(200110475028)；

摘要/Abstract

摘要： In this paper,the higher dimensional conjecture on Veronese generating subman-ifolds proposed by Prof. SUN Zhen-zu is generalized to Pseudo-Euclidean Space L₁^m+2, it is proved that in the higher dimentional Lorentz Space L₁^m+2, the generating submanifolds of an n dimentional submanifold of Pseudo-Riemannian unit sphere S1m is an n+1 dimentional minimal submanifold of S₁^m+1 in L₁^m+2 and is of 1-type in L₁^m+2.

关键词: finit type submanifolds, minimal submanifolds, Veronese generating submani- folds

Abstract: In this paper,the higher dimensional conjecture on Veronese generating subman-ifolds proposed by Prof. SUN Zhen-zu is generalized to Pseudo-Euclidean Space L₁^m+2, it is proved that in the higher dimentional Lorentz Space L₁^m+2, the generating submanifolds of an n dimentional submanifold of Pseudo-Riemannian unit sphere S1m is an n+1 dimentional minimal submanifold of S₁^m+1 in L₁^m+2 and is of 1-type in L₁^m+2.

Key words: finit type submanifolds, minimal submanifolds, Veronese generating submani- folds

中图分类号:

O186.1

宋鸿藻, 宋晓新. 关于Veronese生成子流形的一个猜想[J]. 数学季刊, 2004, 19(1): 63-66.

SONG Hong-zao, SONG Xiao-xin a. A Conjecture on Veronese Generating Submanifolds[J]. Chinese Quarterly Journal of Mathematics, 2004, 19(1): 63-66.

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