Rigidity and Vanishing Theorems for Almost Even-Clifford Hermitian Manifolds

TL;DR

This paper establishes rigidity and vanishing theorems for twisted Dirac operators on almost even-Clifford Hermitian manifolds with circle symmetries, advancing understanding of geometric and topological properties of these manifolds.

Contribution

It introduces new rigidity and vanishing results for indices of natural twisted Dirac operators on a class of manifolds with circle actions.

Findings

Proved rigidity of certain twisted Dirac operator indices.

Established vanishing theorems under specific geometric conditions.

Applied results to almost even-Clifford Hermitian manifolds with automorphism circle actions.

Abstract

We prove the rigidity and vanishing of several indices of "geometrically natural" twisted Dirac operators on almost even-Clifford Hermitian manifolds admitting circle actions by automorphisms.