Equivariant Bismut Laplacian and spectral Einstein functional

TL;DR

This paper develops the spectral Einstein functional using the equivariant Bismut Laplacian on spinor bundles, providing explicit residue density computations and proving related theorems for lower-dimensional manifolds.

Contribution

It introduces the spectral Einstein functional with two vector fields and develops equivariant Bismut Laplacian techniques, extending Dabrowski-Sitarz-Zalecki theorems to lower dimensions.

Findings

Explicit computation of equivariant noncommutative residue density.

Development of spectral Einstein functionals with vector fields.

Proof of equivariant Dabrowski-Sitarz-Zalecki theorems for lower-dimensional manifolds.

Abstract

This paper aims to provide an explicit computation of the equivariant noncommutative residue density of which yield the metric and Einstein tensors on even-dimensional Riemannian manifolds. A considerable contribution of this paper is the development of the spectral Einstein functionals by two vector fields and the equivariant Bismut Laplacian over spinor bundles. We prove the equivariant Dabrowski-Sitarz-Zalecki type theorems for lower dimensional spin manifolds with (or without) boundary.