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


We show, for every Hermitian vector bundle \pi:\,(E,g)\rightarrow (M,h) over a compact Kähler Einstein manifold (M,h), if the projection \pi 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.

DOI Code: 10.1285/i15900932v39n2p95

Keywords: biharmonic maps; harmonic maps; Kähler Einstein manifolds; Hermitian vector bundles

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