John Bland, Tom Duchamp (1995)
Banach Center Publications
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A normal form for small CR-deformations of the standard CR-structure on the (2n+1)-sphere is presented. The space of normal forms is parameterized by a single function on the sphere. For n>1, the normal form is used to obtain explicit embeddings into . For n=1, the cohomological obstruction to embeddability is identified.
Elisabetta Barletta, Sorin Dragomir (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Dmitri Alekseevsky, Yoshinobu Kamishima (2004)
Open Mathematics
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We define notion of a quaternionic and para-quaternionic CR structure on a (4n+3)-dimensional manifold M as a triple (ω1,ω2,ω3) of 1-forms such that the corresponding 2-forms satisfy some algebraic relations. We associate with such a structure an Einstein metric on M and establish relations between quaternionic CR structures, contact pseudo-metric 3-structures and pseudo-Sasakian 3-structures. Homogeneous examples of (para)-quaternionic CR manifolds are given and a reduction construction...
M. Kuranishi (1982-1983)
Séminaire Équations aux dérivées partielles (Polytechnique)
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S. M. Salamon (1986)
Annales scientifiques de l'École Normale Supérieure
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Marian-Ioan Munteanu (2006)
Archivum Mathematicum
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We introduce a torsion free linear connection on a hypersurface in a Sasakian manifold on which we have defined in natural way a -structure of -codimension 2. We study the curvature properties of this connection and we give some interesting examples.
Gerd Schmalz, Jan Slovák (2012)
Open Mathematics
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There are only some exceptional CR dimensions and codimensions such that the geometries enjoy a discrete classification of the pointwise types of the homogeneous models. The cases of CR dimensions n and codimensions n 2 are among the very few possibilities of the so-called parabolic geometries. Indeed, the homogeneous model turns out to be PSU(n+1,n)/P with a suitable parabolic subgroup P. We study the geometric properties of such real (2n+n 2)-dimensional submanifolds in for all n...