Selfdual 4-manifolds, projective surfaces, and the Dunajski-West construction

DOI10.3842/SIGMA.2014.035zbMath1288.53075arXivmath/0606754OpenAlexW2150064105WikidataQ126003093 ScholiaQ126003093MaRDI QIDQ2447893

David M. J. Calderbank

Publication date: 29 April 2014

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0606754

zbMATH Keywords

integrable systemsprojective geometrytwistor theoryselfduality

Mathematics Subject Classification ID

Applications of global differential geometry to the sciences (53C80) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory (83C20) Twistor theory, double fibrations (complex-analytic aspects) (32L25) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Twistor methods in differential geometry (53C28) Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism (83C60) Yang-Mills and other gauge theories in mechanics of particles and systems (70S15) Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics (37K65)

Related Items (12)

Singular self-dual Zollfrei metrics and twistor correspondence ⋮ Complex surfaces and null conformal Killing vector fields ⋮ Geometric theory of Weyl structures ⋮ Gauge theory on projective surfaces and anti-self-dual Einstein metrics in dimension four ⋮ Two-dimensional twistor manifolds and Teukolsky operators ⋮ Anti-self-dual conformal structures with null Killing vectors from projective structures ⋮ Einstein metrics, projective structures and the \(\mathrm{SU}(\infty)\) Toda equation ⋮ Metrisability of projective surfaces and pseudo-holomorphic curves ⋮ The Cayley cubic and differential equations ⋮ A construction of Einstein-Weyl spaces via Lebrun-Mason type twistor correspondence ⋮ Wave equations and the LeBrun-Mason correspondence ⋮ Minimal Lagrangian connections on compact surfaces

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