四维扭化BCV空间的次黎曼极限，带挠率的联络以及Gauss-Bonnet定理

doi:10.13371/j.cnki.chin.q.j.m.2025.02.001

数学季刊 ›› 2025, Vol. 40 ›› Issue (2): 111-134.doi: 10.13371/j.cnki.chin.q.j.m.2025.02.001

• • 下一篇

四维扭化BCV空间的次黎曼极限，带挠率的联络以及Gauss-Bonnet定理

1. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China; 2. Mathematical Science Research Center, Chongqing University of Technology, Chongqing 400054, China

收稿日期:2024-12-10 出版日期:2025-06-30 发布日期:2025-06-12
作者简介:LI Hong-feng (1997-), male, native of Anshan, Liaoning, postgraduate student of Northeast Normal University, engages in global differential geometry; LIU Ke-feng (1965-), male, native of Kaifeng, Henan, professor of Chongqing University of Technology, engages in complex geometry; WANG Yong (1976-), male, native of Changchun, Jilin, professor of Northeast Normal University, engages in global differential geometry.
基金资助:
Supported by National Natural Science Foundation of China (Grant No. 11771070).

ub-Riemannian Limits, Connections with Torsion and the Gauss-Bonnet Theorem for Four Dimensional Twisted BCV Spaces

1. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China; 2. Mathematical Science Research Center, Chongqing University of Technology, Chongqing 400054, China

Received:2024-12-10 Online:2025-06-30 Published:2025-06-12
About author:LI Hong-feng (1997-), male, native of Anshan, Liaoning, postgraduate student of Northeast Normal University, engages in global differential geometry; LIU Ke-feng (1965-), male, native of Kaifeng, Henan, professor of Chongqing University of Technology, engages in complex geometry; WANG Yong (1976-), male, native of Changchun, Jilin, professor of Northeast Normal University, engages in global differential geometry.
Supported by:
Supported by National Natural Science Foundation of China (Grant No. 11771070).

摘要/Abstract

摘要： In this paper, we compute sub-Riemannian limits of some important curvature variants associated with the connection with torsion for four dimensional twisted BCV spaces and derive a Gauss-Bonnet theorem for four dimensional twisted BCV spaces.

关键词: Gauss-Bonnet theorem, Sub-Riemannian limit, Twisted BCV spaces, Orthogonal connections with torsion

Abstract: In this paper, we compute sub-Riemannian limits of some important curvature variants associated with the connection with torsion for four dimensional twisted BCV spaces and derive a Gauss-Bonnet theorem for four dimensional twisted BCV spaces.

Key words: Gauss-Bonnet theorem, Sub-Riemannian limit, Twisted BCV spaces, Orthogonal connections with torsion

中图分类号:

O186.12

李洪峰, 刘克峰, 王勇. 四维扭化BCV空间的次黎曼极限，带挠率的联络以及Gauss-Bonnet定理[J]. 数学季刊, 2025, 40(2): 111-134.

LI Hong-feng, LIU Ke-feng, WANG Yong. ub-Riemannian Limits, Connections with Torsion and the Gauss-Bonnet Theorem for Four Dimensional Twisted BCV Spaces[J]. Chinese Quarterly Journal of Mathematics, 2025, 40(2): 111-134.

[1]	周久儒. 具有加权p-Poincaré不等式的光滑测度空间上的消灭定理[J]. 数学季刊, 2020, 35(3): 311-319.
[2]	纪祥. 完备非紧流形上非齐热方程的椭圆型梯度估计[J]. 数学季刊, 2018, 33(1): 61-67.
[3]	张运涛. 空间形式中的完备子流形[J]. 数学季刊, 2016, 31(3): 298-306.
[4]	邢杰. 紧致流形上Lichnerowicz方程的梯度估计[J]. 数学季刊, 2015, 30(3): 317-322.
[5]	刘玲, 苏农. 关于拟-Jacobi双代数胚及其Dirac-Jacobi结构[J]. 数学季刊, 2014, 29(1): 97-106.
[6]	朱静勇, 宋卫东. 拟常全纯截面曲率空间中的2调和子流形[J]. 数学季刊, 2013, 28(2): 166-171.
[7]	彭慧春. 关于复射影空间中具有平行平均曲率向量的全实叶的注记[J]. 数学季刊, 2011, 26(3): 410-414.
[8]	黄广月, 马冰清. Sasakian空间形式中子流形的全实截面曲率[J]. 数学季刊, 2011, 26(2): 174-178.
[9]	钟定兴, 孙弘安, 慕晓凯 . Sⁿ上子流形的Moebius数量曲率的上界[J]. 数学季刊, 2010, 25(1): 65-73.
[10]	刘建成, 张德燕. de Sitter空间中具有常数量曲率的完备类空子流形[J]. 数学季刊, 2009, 24(3): 357-364.
[11]	刘建成. F-调和映照的稳定性[J]. 数学季刊, 2007, 22(3): 339-343.
[12]	张士诚, 吴报强. 局部对称Lorentz空间中的具有常数量曲率的完备类空超曲面[J]. 数学季刊, 2007, 22(2): 266-275.
[13]	王林峰. 拟常曲率流行中全脐点子流行的拼嵌定理[J]. 数学季刊, 2006, 21(3): 342-350.
[14]	李兴校, 黄广月. 余辛空间形式中的子流形不等式[J]. 数学季刊, 2005, 20(4): 372-379.
[15]	. [J]. 数学季刊, 2005, 20(3): 289-295.

四维扭化BCV空间的次黎曼极限，带挠率的联络以及Gauss-Bonnet定理

ub-Riemannian Limits, Connections with Torsion and the Gauss-Bonnet Theorem for Four Dimensional Twisted BCV Spaces

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价