Differential invariants of self-dual conformal structures

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• 作者：Boris Kruglikov ; ^{boris.kruglikov@uit.no} ; Eivind Schneider ^{eivind.schneider@uit.no}
• 关键词：Differential invariants ; Invariant derivations ; Self-duality ; Conformal metric structure ; Hilbert polynomial ; Poincaré ; function
• 刊名：Journal of Geometry and Physics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：113
• 期：Complete
• 页码：176-187
• 全文大小：456 K
• 卷排序：113

文摘

We compute the quotient of the self-duality equation for conformal metrics by the action of the diffeomorphism group. We also determine Hilbert polynomial, counting the number of independent scalar differential invariants depending on the jet-order, and the corresponding Poincaré function. We describe the field of rational differential invariants separating generic orbits of the diffeomorphism pseudogroup action, resolving the local recognition problem for self-dual conformal structures.