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We consider generalized Hodge-Laplace operators $\alpha d \delta + \beta\delta d$ for $\alpha, \beta > 0$ on $p$-forms on compact Riemannian manifolds.In the case of flat tori and round spheres of different radii, we explicitlycalculate the spectrum of these operators. Furthermore, we investigate underwhich circumstances they are isospectral.

Spectrum of generalized Hodge-Laplace operators on flat tori and round spheres