数学季刊 ›› 2026, Vol. 41 ›› Issue (3): 269-298.doi: 10.13371/j.cnki.chin.q.j.m.2026.03.004

• • 上一篇    下一篇

J统计de Rham Hodge 算子及相关的 Kastler-Kalau-Walze 类型定理

  

  1. 1 . School of Mathematics, Ineer Mongolia Minzu University, TongLiao 028005, China; 2 . School of  Physics and Electronics Information, Ineer Mongolia Minzu University, TongLiao 028005, China
  • 收稿日期:2026-04-23 出版日期:2026-09-30 发布日期:2026-09-30
  • 作者简介:BAO Kai-hua (1984-), female, native of Tongliao, Inner Mongolia, associate professor of Inner  Mongolia Minzu University, engages in differential geometry; CHENG Yu-mei (1984-), female, native of Tongliao,  Inner Mongolia, lecturer of Inner Mongolia Minzu University, engages in theoretical physics; SUN Yan-hong (1984-), female, native of Tongliao, Inner Mongolia, lecturer of Inner Mongolia Minzu University, engages in  differential geometry. 
  • 基金资助:
    Supported by Inner Mongolia Natural Science Foundation (Grant No. 2025MS01039) . 

J-Statistical de Rham Hodge Operator and Related Kastler-Kalau-Walze Type Theorems

  1. 1 . School of Mathematics, Ineer Mongolia Minzu University, TongLiao 028005, China; 2 . School of  Physics and Electronics Information, Ineer Mongolia Minzu University, TongLiao 028005, China
  • Received:2026-04-23 Online:2026-09-30 Published:2026-09-30
  • About author:BAO Kai-hua (1984-), female, native of Tongliao, Inner Mongolia, associate professor of Inner  Mongolia Minzu University, engages in differential geometry; CHENG Yu-mei (1984-), female, native of Tongliao,  Inner Mongolia, lecturer of Inner Mongolia Minzu University, engages in theoretical physics; SUN Yan-hong (1984-), female, native of Tongliao, Inner Mongolia, lecturer of Inner Mongolia Minzu University, engages in  differential geometry. 
  • Supported by:
    Supported by Inner Mongolia Natural Science Foundation (Grant No. 2025MS01039) . 

PDF (PC)

0

摘要：  In this paper, we define the basic notions of the J-statistical de Rham Hodge  operator and derive its Lichnerowicz-type formula on compact Riemannian manifolds  without boundary, and establish the Kastler-Kalau-Walze type theorems related to this  operator on four-dimensional and six-dimensional almost product Riemannian manifolds  with boundary.

关键词:  J-statistical de Rham Hodge operator, Noncommutative residue, Gravita-tional action, Kastler-Kalau-Walze type theorems

Abstract:  In this paper, we define the basic notions of the J-statistical de Rham Hodge  operator and derive its Lichnerowicz-type formula on compact Riemannian manifolds  without boundary, and establish the Kastler-Kalau-Walze type theorems related to this  operator on four-dimensional and six-dimensional almost product Riemannian manifolds  with boundary.

Key words:  J-statistical de Rham Hodge operator, Noncommutative residue, Gravita-tional action, Kastler-Kalau-Walze type theorems

中图分类号: 

版权所有 © 《数学季刊》编辑部
地址：河南省开封市明伦街85号河南大学数学季刊编辑部
电话：0371-23881698　E-mail: sxjk@henu.edu.cn　QQ: 2454327236
本系统由北京玛格泰克科技发展有限公司设计开发　技术支持：support@magtech.com.cn