Let $(M,g)$ be an oriented, real analytic, Riemannian $n$-manifold without boundary. Let $\Delta_k=(d+\delta)^2$ denote the Laplace-Beltrami operator acting on (smooth) $k$-forms. I am looking for a reference of the following:
Let $\omega$ be a (smooth) $k$-form satisfying $\Delta_k \omega=\lambda \omega$ for some constant $\lambda\in \mathbb{R}$, then $\omega$ is real analytic.
I know its true on the level of $0$-forms, but I couldn't find any source dealing with the case of general $k$-forms.
Any help is greatly appreciated.
Kind Regards
Dennis