Finding a solutions for an equation

dg.differential geometry – Reference for non-parallel harmonic $okay$-forms retort

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dg.differential geometry – Reference for non-parallel harmonic $okay$-forms

I wish to purchase some abysmal judgement on closed orientable Riemannian manifolds admitting $okay$-forms ($kgeq 2$) $omega$ that satisfices the next situations:
$$nabla omeganeq 0,quad Deltaomega=0.$$
the place $Delta=(delta +d)^2$ is the Laplace-Beltrami operator (Hodge Laplacian). What different helpful properties can these varieties maintain? Any reference would breathe vastly appreciated.

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