The noncommutative residue and sub-Riemannian limits for the twisted BCV spaces

TL;DR

This paper extends the Kastler-Kalau-Walze and Dabrowski-Sitarz-Zalecki theorems to twisted BCV spaces, analyzing their sub-Riemannian geometry and computing related Connes invariants.

Contribution

It introduces sub-Riemannian versions of key theorems and computes Connes invariants for twisted BCV spaces, advancing noncommutative geometric analysis.

Findings

Derived sub-Riemannian Kastler-Kalau-Walze theorem

Computed Connes conformal invariants for twisted products

Analyzed sub-Riemannian limits of invariants

Abstract

In this paper, we derive the sub-Riemannian version of the Kastler-Kalau-Walze 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.