Biharmonic Hermitian vector bundles over compact Kähler manifolds and compact Einstein Riemannian manifolds

Abstract

We show, for every Hermitian vector bundle over a compact Kähler Einstein manifold , if the projection is biharmonic, then it is harmonic. On a biharmonic Hermitian vector bundle over a compact Riemannian manifold with positive Ricci curvature, we show a new estimate of the first eigenvalue of the Laplacian.