Statistical de Rham Hodge operators and the Kastler-Kalau-Walze type theorem for manifolds with boundary

TL;DR

This paper establishes Lichnerowicz formulas and proves Kastler-Kalau-Walze type theorems for statistical de Rham Hodge operators on compact manifolds with boundary, extending geometric analysis in this context.

Contribution

It introduces Lichnerowicz formulas and proves Kastler-Kalau-Walze theorems for statistical de Rham Hodge operators on manifolds with boundary, a novel extension in geometric analysis.

Findings

Lichnerowicz type formulas derived for statistical de Rham Hodge operators

Kastler-Kalau-Walze type theorems proved for manifolds with boundary

Extension of geometric analysis results to statistical de Rham Hodge operators

Abstract

In this paper, we give the Lichnerowicz type formulas for statistical de Rham Hodge operators. Moreover, Kastler-Kalau-Walze type theorems for statistical de Rham Hodge operators on compact manifolds with (respectively without) boundary are proved.