Spinorially twisted Spin structures, I: curvature identities and eigenvalue estimates

TL;DR

This paper introduces higher rank spinorially twisted spin structures, deriving curvature identities and eigenvalue estimates for associated twisted Dirac operators, advancing understanding in spin geometry.

Contribution

It defines new spinorially twisted structures and establishes curvature identities and eigenvalue bounds for their Dirac operators.

Findings

Derived curvature identities for twisted spin structures

Established eigenvalue estimates for twisted Dirac operators

Introduced higher rank spinorially twisted spin structures

Abstract

We define (higher rank) spinorially twisted spin structures and deduce various curvature identites as well as estimates for the eigenvalues of the corresponding twisted Dirac operators.