Specificity of Petrov classification of (anti-)self-dual zero signature metrics

DOI10.3103/S1066369X20090054zbMath1477.53030OpenAlexW3093196967MaRDI QIDQ2027831

L. N. Krivonosov, V. A. Luk'yanov

Publication date: 28 May 2021

Published in: Russian Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s1066369x20090054

zbMATH Keywords

Weyl tensorPetrov classificationself dualityHodge operatoranti-self duality

Mathematics Subject Classification ID

Hodge theory in global analysis (58A14) Local differential geometry of Lorentz metrics, indefinite metrics (53B30) Conformal structures on manifolds (53C18)

Related Items (2)

Эрмитовы метрики с (анти)автодуальным тензором Римана ⋮ (Anti-)self-dual Einsteinian metrics of zero signature, their Petrov classes and connection with Kähler and para-Kähler structures

Cites Work

• The main theorem for (anti-)self-dual conformal torsion-free connection on a four-dimensional manifold
• On the Einstein-Weyl and conformal self-duality equations
• Self-duality in four-dimensional Riemannian geometry
• Some local aspects of the theory of conformal structure
• On the self-duality of the Weyl tensor using Ashtekar's variables
• Уравнения дуальности на 4-многообразии конформной связности без кручения и некоторые их решения для нулевой сигнатуры
• The inverse spectral transform for the Dunajski hierarchy and some of its reductions: I. Cauchy problem and longtime behavior of solutions
• Dunajski generalization of the second heavenly equation: dressing method and the hierarchy

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