Spectra and symmetric eigentensors of the Lichnerowicz Laplacian on $P^n(\comp)$

TL;DR

This paper calculates the eigenvalues and eigentensors of the Lichnerowicz Laplacian on complex symmetric tensor fields over complex projective space, providing explicit descriptions of these spectral components.

Contribution

It offers the first explicit computation of eigenvalues and eigentensors of the Lichnerowicz Laplacian on complex projective spaces, including multiplicities.

Findings

Eigenvalues with multiplicities are explicitly computed.

Spaces of symmetric eigentensors are explicitly characterized.

Provides a detailed spectral decomposition for the Lichnerowicz Laplacian.

Abstract

We compute the eigenvalues with multiplicities of the Lichnerowicz Laplacian acting on the space of complex symmetric covariant tensor fields on the complex projective space $P^n(\comp)$. The spaces of symmetric eigentensors are explicitly given.