非交换留数和扭化BCV空间的次黎曼极限

李洪峰, 刘克峰, 王勇

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

数学季刊 >

2026 , Vol. 41 >Issue 1: 15 - 37

DOI: https://doi.org/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

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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

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.

收稿日期: 2025-06-05

网络出版日期: 2026-03-30

基金资助

Supported by National Natural Science Foundation of China (Grant No. 11771070).

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

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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

WANG Yong (1976-), male, native of Changchun, Jilin, professor of Northeast Normal University, engages in global differential geometry.

Received date: 2025-06-05

Online published: 2026-03-30

Supported by

Supported by National Natural Science Foundation of China (Grant No. 11771070).

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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

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

Abstract

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

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