On the kernel of the maximal flat Radon transform on symmetric spaces of compact type

الأصل · EN

Let M be a Riemannian globally symmetric space of compact type, M' its set of maximal flat totally geodesic tori, and ad(M) its adjoint space. We show that the kernel of the maximal flat Radon transform τ:L²(M) → L²(M') is precisely the orthogonal complement of the image of the pullback map L²(ad(M))→ L²(M). In particular, we show that the maximal flat Radon transform is injective if and only if M coincides with its adjoint space.