Abstract: 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 H p,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 (S 2p–1 × S 2q–1)/Z 2. inside the real projective space P(E 1), where E 1 is the real 2n-dimensional space subordinate to H p,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 H p,q, inside the complex projective space P(H p,q), diffeomorphic to (S 2p–1 × S 2q–1)/S 1. 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 H p,q. It is shown how a distribution y → D y, where $${y \in H\backslash\{0\},H}$$ being the isotropic cone of H p,q allows to $${\widetilde{H_{p+1,q+1}}}$$ to be considered as a "special pseudo-unitary conformal compactified" of H p,q × R. The following results precise the presentation given in [1,c].

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{{Explor lien
   |wiki=    Wicri/Mathematiques
   |area=    BourbakiV1
   |flux=    France
   |étape=   Analysis
   |type=    RBID
   |clé=     ISTEX:D07C3E0A34F574F14927A291BDC824F41E98A7DE
   |texte=   Study of Some Fundamental Projective Quadrics Associated with a Standard Pseudo-Hermitian Space H p , q
}}