Algebraically special, real alpha-geometries

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• 作者：Peter R. Law^a ; ^{prldb@member.ams.org"" rel=""nofollow} ; ^{prldb@yahoo.com"" rel=""nofollow} ; Yasuo Matsushita^b ; ^{matsushita.y@e.usp.ac.jp"" rel=""nofollow}
• 关键词：Neutral geometry ; Walker geometry ; Weyl curvature ; Four dimensions ; Spinors
• 刊名：Journal of Geometry and Physics
• 出版年：2011
• 出版时间：November 2011
• 年：2011
• 卷：61
• 期：11
• 页码：2064-2080
• 全文大小：326 K

文摘

We exploit the spinor description of four-dimensional Walker geometry, and conformal rescalings of such, to describe the local geometry of four-dimensional neutral geometries with algebraically degenerate self-dual Weyl curvature and an integrable distribution of α-planes (algebraically special real α-geometry). In particular, we determine the behaviour of Walker geometry under conformal rescaling and provide a derivation of the hyperheavenly equation from conformal rescaling formulae.