The spectrum of the 6-Laplacian on Kähler manifolds. (English) Zbl 0654.53063

In this paper compact, connected Kähler manifolds are considered whose spectra of the Laplacian acting on the 6-forms coincide. It is shown that one of them is of real constant holomorphic sectional curvature \(h\) if and only if the other is of real constant sectional curvature \(h'\) and \(h'=h\), provided their complex dimension n satisfies \(n=4,5\) or \(7\leq n\leq 12\) or \(18\leq n\leq 264\). A similar result is established for Kähler-Einstein manifolds.


53C55 Global differential geometry of Hermitian and Kählerian manifolds
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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