On quaternionic contact Fefferman spaces

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• 作者：Jesse Alt
• 关键词：Quaternionic contact manifolds ; Conformal holonomy ; Fefferman spaces ; Parabolic geometry
• 刊名：Differential Geometry and its Applications
• 出版年：2010
• 出版时间：August 2010
• 年：2010
• 卷：28
• 期：4
• 页码：376-394
• 全文大小：425 K

文摘

We investigate the Fefferman spaces of conformal type which are induced, via parabolic geometry, by the quaternionic contact (qc) manifolds introduced by O. Biquard. Equivalent characterizations of these spaces are proved: as conformal manifolds with symplectic conformal holonomy of the appropriate signature; as pseudo-Riemannian manifolds admitting conformal Killing fields satisfying a conformally invariant system of conditions analogous to G. Sparling's criteria for CR Fefferman spaces; and as the total space of a SO(3)- or S³-bundle over a qc manifold with the conformally equivalent metrics defined directly by Biquard. Global as well as local results are acquired.