The twisted Spin$^c$ Dirac operator on K\"ahler submanifolds of the complex projective space

TL;DR

This paper estimates eigenvalues of the twisted Dirac operator on Kähler submanifolds of complex projective space and examines the sharpness of these estimates for specific embeddings.

Contribution

It provides new eigenvalue estimates for the twisted Dirac operator on Kähler submanifolds of complex projective space and analyzes their sharpness in particular cases.

Findings

Eigenvalue bounds for the twisted Dirac operator on Kähler submanifolds

Sharpness analysis for the embedding $CP^d o CP^m$

Insights into spectral properties of Dirac operators in complex geometry

Abstract

In this paper, we estimate the eigenvalues of the twisted Dirac operator on K\"ahler submanifolds of the complex projective space $CP^m$ and we discuss the sharpness of this estimate for the embedding $CP^d \hookrightarrow CP^m$.