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The Cayley Cubic and Differential Equations

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KRYNSKI Wojciech MAKHMALI Omid

Rok publikování 2021
Druh Článek v odborném periodiku
Časopis / Zdroj The Journal of Geometric Analysis
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www https://doi.org/10.1007/s12220-020-00525-9
Doi http://dx.doi.org/10.1007/s12220-020-00525-9
Klíčová slova Causal geometry; Conformal geometry; Path geometry; Integrable systems; Half-flatness; Lax pair; Cayley's ruled cubic
Popis We define Cayley structures as a field of Cayley's ruled cubic surfaces over a four dimensional manifold and motivate their study by showing their similarity to indefinite conformal structures and their link to differential equations and the theory of integrable systems. In particular, for Cayley structures an extension of certain notions defined for indefinite conformal structures in dimension four are introduced, e.g., half-flatness, existence of a null foliation, ultra-half-flatness, an associated pair of second order ODEs, and a dispersionless Lax pair. After solving the equivalence problem we obtain the fundamental invariants, find the local generality of several classes of Cayley structures and give examples.
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