## 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.

### MSC:

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