This self-contained short note deals with the study of the properties of some real projective compact quadrics associated with a a standard pseudo-hermitian space Hp,q, namely \({\widetilde{Q(p, q)}, \widetilde{Q_{2p+1,1}}, \widetilde{Q_{1,2q+1}}, \widetilde{H_{p,q}}. \, \widetilde{Q(p, q)}}\) is the (2n – 2) real projective quadric diffeomorphic to (S2p–1 × S2q–1)/Z2. inside the real projective space P(E1), where E1 is the real 2n-dimensional space subordinate to Hp,q. The properties of \({\widetilde{Q(p, q)}}\) are investigated. \({\widetilde{H_p,q}}\) is the real (2n – 3)-dimensional compact manifold-(projective quadric)- associated with Hp,q, inside the complex projective space P(Hp,q), diffeomorphic to (S2p–1 × S2q–1)/S1. The properties of \({\widetilde{H_{p,q}}}\) are studied. \({\widetilde{Q_{2p+1,1}}}\) is a 2p-dimensional standard real projective quadric, and \({\widetilde{Q_{1,2q+1}}}\) is another standard 2q-dimensional projective quadric. \({\widetilde{Q_{2p+1,1}} \cup \widetilde{Q_{1,2q+1}}}\), union of two compact quadrics plays a part in the understanding of the "special pseudo-unitary conformal compactification" of Hp,q. It is shown how a distribution y → Dy, where \({y \in H\backslash\{0\},H}\) being the isotropic cone of Hp,q allows to \({\widetilde{H_{p+1,q+1}}}\) to be considered as a "special pseudo-unitary conformal compactified" of Hp,q × R. The following results precise the presentation given in [1,c].