# Biharmonic Hermitian vector bundles over compact Kaehlar Einstein manifolds

## TL;DR

This paper proves that on compact Kaehler Einstein manifolds, biharmonic projections of Hermitian vector bundles are necessarily harmonic, revealing a rigidity property of such geometric structures.

## Contribution

It establishes a new result linking biharmonic and harmonic projections in Hermitian vector bundles over compact Kaehler Einstein manifolds.

## Key findings

- Biharmonic projections are harmonic in this setting
- The result applies to all Hermitian vector bundles over the given manifolds
- Provides insight into the geometric structure of vector bundles on Einstein manifolds

## Abstract

In this paper, we show that, for every Hermitian vector bundle over a compact Kaehler Einstein manifold, if the projection is biharmonic, then it is harmonic.