Conjecture on CR maps preserving the Tanaka–Webster Ricci tensor in generalized ellipsoids

Let the model be the generalized ellipsoid described in Section 2, equipped with the contact form $\vartheta$ defined in equation (polo). A CR map is said to preserve the Tanaka–Webster Ricci tensor when, for its associated conformal factor, the additional Ricci terms in the conformal transformation formula vanish. Ricci-preservation conjecture. Every CR map in this model preserves the Tanaka–Webster Ricci tensor associated with the contact form $\vartheta$. The conjecture proposes that all CR symmetries of the generalized ellipsoid preserve this pseudohermitian curvature tensor, a condition intended to constrain and aid the classification of CR mappings. The source provides no evidence of a resolution.