非交换留数和扭化BCV空间的次黎曼极限

doi:10.13371/j.cnki.chin.q.j.m.2026.01.002

数学季刊 ›› 2026, Vol. 41 ›› Issue (1): 15-37.doi: 10.13371/j.cnki.chin.q.j.m.2026.01.002

非交换留数和扭化BCV空间的次黎曼极限

1. School of Mathematics and Systems Science, Shenyang Normal University, Shenyang 110034, China; 2. Mathematical Science Research Center, Chongqing University of Technology, Chongqing 400054, China; 3. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

收稿日期:2025-06-05 出版日期:2026-03-30 发布日期:2026-03-30
作者简介:LI Hong-feng (1997-), male, native of Anshan, Liaoning, lecturer of Shenyang 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).

The Noncommutative Residue and Sub-Riemannian Limits for the Twisted BCV Spaces

1. School of Mathematics and Systems Science, Shenyang Normal University, Shenyang 110034, China; 2. Mathematical Science Research Center, Chongqing University of Technology, Chongqing 400054, China; 3. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

Received:2025-06-05 Online:2026-03-30 Published:2026-03-30
About author:LI Hong-feng (1997-), male, native of Anshan, Liaoning, lecturer of Shenyang 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 derive the sub-Riemannian version of the Kastler-KalauWalze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for the twisted BCV spaces. We also compute the Connes conformal invariants for the twisted product, as well as the sub-Riemannian limits of the Connes conformal invariants for the twisted BCV spaces.

关键词: Scalar curvature, Sub-Riemannian limit, Conformal invarints, Twisted BCV spaces, Kastler-Kalau-Walze type theorems, Dabrowski-Sitarz-Zalecki type theorems

Abstract: In this paper, we derive the sub-Riemannian version of the Kastler-KalauWalze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for the twisted BCV spaces. We also compute the Connes conformal invariants for the twisted product, as well as the sub-Riemannian limits of the Connes conformal invariants for the twisted BCV spaces.

Key words: Scalar curvature, Sub-Riemannian limit, Conformal invarints, Twisted BCV spaces, Kastler-Kalau-Walze type theorems, Dabrowski-Sitarz-Zalecki type theorems

中图分类号:

O186.12

李洪峰, 刘克峰, 王勇. 非交换留数和扭化BCV空间的次黎曼极限[J]. 数学季刊, 2026, 41(1): 15-37.

LI Hong-feng, LIU Ke-feng, WANG Yong. The Noncommutative Residue and Sub-Riemannian Limits for the Twisted BCV Spaces[J]. Chinese Quarterly Journal of Mathematics, 2026, 41(1): 15-37.

[1]	关庄丹, 闫笑峰. 常黎曼数量曲率Hermitian结构中的临界Hermitian度量研究[J]. 数学季刊, 2026, 41(1): 1-14.
[2]	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.
[3]	陈伟, 郭震. de Sitter空间中类空子流形的刚性定理[J]. 数学季刊, 2010, 25(3): 360-365.
[4]	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.
[5]	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.
[6]	宋鸿藻, 吴报强, 贺慧霞. Quasi-con form ally Flat Manifolds with Constant Scalar Curvature[J]. 数学季刊, 1998, 13(4): 1-6.

非交换留数和扭化BCV空间的次黎曼极限

The Noncommutative Residue and Sub-Riemannian Limits for the 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 6

编辑推荐

Metrics

本文评价