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.
![\pi:\,(E,g)\rightarrow (M,h)](http://212.189.136.205/plugins/generic/latexRender/cache/8a76f5a7380ee34c79ea8f4a43b706be.png)
![(M,h)](http://212.189.136.205/plugins/generic/latexRender/cache/ae215a7b9ba17ee21d1687f96886823c.png)
![\pi](http://212.189.136.205/plugins/generic/latexRender/cache/4f08e3dba63dc6d40b22952c7a9dac6d.png)
DOI Code:
10.1285/i15900932v39n2p95
Keywords:
biharmonic maps; harmonic maps; Kähler Einstein manifolds; Hermitian vector bundles
Full Text: PDF