A Lichnerowicz vanishing theorem for proper cocompact actions

TL;DR

This paper proves a vanishing theorem for certain non-compact spin manifolds with proper cocompact group actions, extending classical results to new geometric contexts involving unimodular groups.

Contribution

It introduces a Lichnerowicz type vanishing theorem applicable to non-compact spin manifolds with proper cocompact actions by unimodular groups, broadening the scope of classical results.

Findings

Vanishing of certain Dirac operator indices under specified conditions

Extension of Lichnerowicz theorem to non-compact manifolds with group actions

Applicability to unimodular group actions on spin manifolds

Abstract

We establish a Lichnerowicz type vanishing theorem for non-compact spin manifolds admiting proper cocompact actions, when the action group is unimodular.