Abstract
Covering groups of the conformal pseudo-unitary groups are given. Conformal flat pseudo-unitary geometry is studied. Two fundamental diagrams are given. We introduce and give geometrical characterizations of groups called pseudo-unitary conformal spinoriality groups. The study of pseudo-unitary spin structures and conformal pseudo-unitary spin structures over an almost complex 2n-dimensional manifold V is now presented. The part played by groups called pseudo-unitary conformal groups is emphasized. The links between pseudo-unitary spin structures and pseudo-unitary conformal spin ones are given.
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