Let $(\mathcal{M},g)$ be a Riemannian manifold and $\Delta_g$ be the corresponding Laplace Beltrami operator. The Laplace Beltrami operator can be applied to tensor fields. Do we also get some results about eigentensor-fields being an orthogonal basis of tensor fields?
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Some time ago I ran across this paper which deals with the case of the sphere. (I found it mostly indecipherable, though) – Giuseppe Negro Jan 09 '18 at 21:06
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A bit late but thank you Giuseppe. – Chevallier Aug 04 '19 at 16:50
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You are welcome. I hope you could understand something of that paper. I still cannot. :) – Giuseppe Negro Aug 05 '19 at 10:18